Gemara

(Mishnah): If he had an extra finger or toe and it was cut off, if it had a bone, he is Pasul (a Ba'al Mum).

Bava Kama 90b (Mishnah): A case occurred in which a man uncovered a woman's head in the market. R. Akiva obligated him to pay 400 Zuz.

The man broke a small flask of oil in front of her. She uncovered her hair, and was Metapachas (hitting or dabbing) and putting her hand on her head (to dab the oil into her hair).

R. Akiva: Even so, you must pay. One may not injure himself, but if he does, he is exempt. Others may not injure him, but if they do, they are liable.

91a - Contradiction (Beraisa - R. Akiva): A person may injure himself.

Answer #1 (Rava): A person may not bodily injure himself, but he may embarrass himself.

Question: The Mishnah discusses embarrassment, and R. Akiva said that one may not injure himself!

Answer: He said that not only regarding embarrassment, in which Reuven may embarrass himself, (even if Reuven does so) if Shimon embarrasses him he is liable. Rather, even regarding bodily damage, in which Reuven may not damage himself, (even if Reuven damages himself,) if Shimon damages him, he is liable.

Question (Beraisa): "To harm or to benefit..." includes one who swore to harm himself (he is liable if he does not do so. This shows that one may harm himself.)

Answer (and Answer #2 to the Contradiction): Tana'im argue about this. (Each Tana says that R. Akiva agrees with him.)

Suggestion: R. Elazar forbids a person to damage himself. He says that one who tears too much clothing out of grief over a death transgresses 'Bal Tashchis'. All the more so, one who damages his body transgresses!

Rejection: Perhaps damaging one's body is less severe, for the damage can heal, unlike tearing clothing.

When Rav Chisda would walk among thorns, he would lift his garment, because damage to the body heals, but damage to clothes does not heal.

Answer #2: It is R. Elazar Hakapar b'Ribi:

(Beraisa - R. Elazar Hakapar): "Me'Asher Chota Al ha'Nefesh" - a Nazir sinned against his own soul, by denying himself wine. All the more so one who (fasts and) denies himself all food is called a sinner!

Makos 20b (Beraisa) Suggestion: Perhaps "v'Seret" applies even if he scratches (and wounds) himself because his house burned down or his ship sank!

Rejection: "La'Nefesh" teaches that he is liable only due to a Mes.

Sanhedrin 68a: They carried R. Eliezer's coffin from Keisari to Lud. R. Akiva was wounding himself. His blood was spilling on the ground;

He said 'I have many coins, and no moneychanger to look at them! (No one else can answer my questions.)

Rishonim

Rambam (Hilchos Chovel u'Mazik 5:1): One may not wound himself or another. Even without wounding, a Lav forbids hitting a Kosher Yisrael in a hostile way.

Rosh (Mo'ed Katan 3:93): One is liable for Seritah only through scratching, but not through beating himself. We find that R. Akiva wounded himself over the death of R. Eliezer. This is astounding. Since it is forbidden by hand or through a Kli, why may one beat himself?! Tosfos answers that he did so due to the Torah. He was saying 'I have many coins...'

Tosfos (91b DH Ela Hai): The Gemara proved that one may not wound himself even for a need, e.g. the woman who was dabbing her head, or one who killed himself due to something he feared, or one who tore too much in grief over a Mes. This is for a need (and even so, it is forbidden).

Tosfos Yom Tov (Bava Kama 8:6 DH v'Haysah): Some texts of the Rif (Bava Kama 32a) say that she was Metapachas and Makah (hitting) her head. If so we must say that it was her oil, and she agonized over her loss. However, Avos d'R. Noson says that it was not her oil, and Tosfos says that what she did was for a need. Perhaps these texts of the Rif should say that she was Metapachas and Sachah (anointing) her head

Tosfos (Yevamos 13b DH d'Amar): R. Akiva wounded himself over the death of R. Eliezer until his blood flowed to the ground/ R. Yitzchak says that the Isur is only through scratching. Alternatively, he did so out of pain over the loss of Torah.

Poskim

Shulchan Aruch (CM 420:31): Even though one may not wound himself, if he did, he is exempt.

Tur (CM 420:31): One may not wound himself. The Ramah says that the Halachah is that one may.

Prishah (21 DH Kosav): Even though one may not tear too many garments due to a Mes, all agree that there is more Heter to wound the body, for it heals, unlike garments.

Yam Shel Shlomo (Bava Kama 8:59): One may not harm or embarrass himself for monetary gain. The Gemara concluded that Tana'im argue about whether one may harm himself. We retract from Rava's answer; shame is like bodily damage. The Tur brings from the Ramah that the Halachah permits wounding oneself. The Beraisa of R. Elazar Hakapar is a mere Drashah. It does not discuss wounding. Even the Ramah permits only for a need. One may not harm even garments or other matters (without a need), due to 'Bal Tashchis.' It is permitted for needs of the body. Bal Tashchis of the body overrides Bal Tashchis of property (Shabbos 129a). Likewise, one may destroy property for a need, e.g. to instill fear in one's house (Shabbos 108b). Likewise, one may wound his body for a need. I say that the Halachah follows our Mishnah, which forbids. The Rif and Rosh (Bava Kama 32a and 8:13) simply bring the Mishnah. If so, it is forbidden even for a need. The Mishnah discusses a monetary need, and R. Akiva said that one may not wound himself.

Rema (YD 180:6): Seritah is permitted over pain other than a Mes.

Beis Yosef (DH u'Mah): In Makos we forbid only due to a Mes.

Beis Yosef (DH ha'Mesaret): The Tur says that one who scratches over other pains is exempt. It seems that there is no Isur at all.

Shulchan Aruch (YD 180:7): Some say that only scratching (over a Mes) is forbidden, but one may hit himself with his hand until his blood flows. Some forbid.

Shach (10): This is if one does so due to the Mes. If one does so for Torah, i.e. a Gadol died and one is pained over the (loss of) Torah, it is permitted (Rosh and Tur).

Aruch l'Ner (Yevamos 13b DH d'Amar): Tosfos in Sanhedrin and the Tur (YD 180) bring only the latter answer of Tosfos in Yevamos. The Poskim proved from this question that it is permitted for the sake of Torah. I ask against both answers. R. Akiva himself forbids wounding oneself! Tosfos says that we concluded that Tana'im argue about his opinion, but it is difficult to say that one opinion would deny that he wounded himself over the death of R. Eliezer! When a king dies, we cut off the legs of his animals. Tosfos (Avodah Zarah 11a Okrin) says that this is not Bal Tashchis, since it is for the king's honor. The Isur to wound oneself comes from Bal Tashchis, therefore it is permitted for the sake of honor. If not for the Rishonim, I would have said that R. Akiva did not intend to wound himself. He was greatly distressed. When he realized that he was wounding himself, he ceased! It is forbidden even for pain and the honor of Torah. Do not say that a Tzadik would not stumble in sin. This applies only to eating Isur. Also Rava wounded himself unintentionally (Shabbos 88a). In Avos d'R. Noson (25:3) it says that R. Akiva tore his clothes and pulled his hair, and his blood flowed. It does not say that he hit himself. Also in Sanhedrin, it does not mean that he intentionally hit himself. I disagree with the Shach.

Rebuttal (Igros Moshe CM 2:66): This is not honor of the Torah. The Torah does not desire this. Tosfos did not mention honor of Torah, rather, that R. Akiva was pained over the loss of Torah. Also, this does not explain why the Beis Yosef and Rema (Saif 6) permit for other pains. Rather, we must say like I explain (it is permitted if it assuages his pain).

Igros Moshe (ibid.): A girl wants to do cosmetic surgery to become a more appealing Shiduch. In Bava Kama we forbid wounding oneself, even for a need, e.g. to gain a small amount of oil. Even though here it is a great need, Chazal did not distinguish between small and great needs. However, we concluded that the Isur to harm oneself is like R. Elazar Hakapar, who holds that a Nazir is a sinner. Presumably, if he received a monetary or other benefit from abstaining from wine, it would be permitted. If so, one may harm himself for a gain, even though the Isur was learned from a Kal va'Chomer. What is Tosfos' source to forbid even for a need? We must say that abstaining from wine for a need is not called pain at all, since his Hana'ah (from his gain) exceeds his pain. If he would drink, he would be pained by losing his gain. This exceeds his pain from not drinking! The pain is due only to his desire, and he desires the gain more! Wounding causes a real pain, which is not due to desire. It is not traded for pain of not gaining, which is only from desire for gain. One may not do so. The Halachah does not follow R. Elazar Hakapar, yet the Rambam forbids wounding oneself, like the Gra (YD 236:6) brings. We must say that another source forbids even for a need. In any case, if we would have needed to say that R. Elazar Hakapar permits for a need, this would have been a proof according to everyone, for we do not find anyone who argues. In the Mishnah, R. Akiva forbids wounding oneself even for a need. Therefore we must say like I said. The Rambam forbids hitting a Yisrael in a hostile way; some texts say 'in a degrading way.' These do not apply here, for it is to beautify her. Since others may hit her in this way, she may do so to herself.

Igros Moshe: Rav Chisda is a proof for the Rambam. Even if he intended only to save his clothes, but not to wound himself, it was a Pesik Reishei. It is difficult to say that it was not a Pesik Reishei. We must say that the Isur when one intends for a need is only if he intends for pain, e.g. tearing over a Mes. If so, we must forbid also one who wounds himself, e.g. scratches himself over a Mes. However, if so, why do we exempt one who wounds himself due to other pains, e.g. his house fell or his boat sank (Makos 20b)? It is difficult to say that the Torah gave an extra Lav specifically for scratching over a Mes. R. Akiva wounded himself over the death of R. Eliezer Tosfos explains that he did so due to the loss of Torah. It should be forbidden in any case due to wounding himself! We must say that this assuaged his pain, like Rashi (Shabbos 105b) explains regarding tearing garments over a Mes.

Igros Moshe (DH u'Ktzas): In Bechoros, we say that if one had an extra finger and cut it off (this is a Mum). If this were forbidden, the Mishnah should have said 'even though one may not do so', like it says about selling a donkey to Nochrim. It is difficult to say that this is like the Tana who argues with R. Akiva. Rather, since he does so to beautify himself, it is permitted. The same applies to plastic surgery for a woman, since we say (Kesuvos 59b) that women are for beauty.