Gemara

(Beraisa - R. Yehudah): "U'Ma'uch v'Chasus v'Nasuk v'Charus" all apply to the Beitzim (testicles).

All the more so, they apply to the Ever (it is more exposed than the Beitzim).

R. Eliezer ben Yakov says, all apply (only) to the Ever;

R. Yosi says, Ma'uch and Kasus apply even to the Beitzim. Nasuk and Karus apply to the Ever.

Chagigah 14b - Question: May one castrate a dog?

Answer (Ben Zoma): "Uv'Artzechem Lo Sa'asu" - do not do this to anything in your land.

Shabbos 110b: To cure jaundice, one drinks two (ingredients mentioned above) in beer. This (also) causes sterility.

Question: This is forbidden!

(Beraisa - R. Chanina): One may not castrate a person. We read "uV'ArtzeCHEM Lo Sa'asu" like 'BACHEM Lo SE'asu' (do not become sterile).

Answer #1: A Seris (one who was already castrated) may use this cure.

Objection: R. Chiya bar Aba taught that all agree that one is liable for Mechametz after Mechametz (of Menachos), for it says "Lo Se'aseh Chometz" and "Lo Se'afeh Chometz" (to obligate for every step of baking, even if the dough already became Chometz);

All agree that one is liable for castration after castration - "u'Ma'uch v'Chasus v'Nasuk v'Charus (... uv'Artzechem Lo Sa'asu)";

Answer #2: Someone too old to have children may use this cure.

Objection: R. Yochanan said 'these (cures discusses in Gitin) returned me to my youth (fertility)!'

Answer #3: A woman may use this cure.

Question: R. Yochanan ben Berokah holds that "va'Yomer Lahem Peru u'Rvu" was said also to women. (Also they are also commanded to have children.). How can he answer?

Answer #4: A woman who is sterile or too old to have children may use this cure.

Yevamos 65b (Mishnah): A man is commanded about Peru u'Rvu, but not a woman;

R. Yochanan ben Brokah says, "Peru u'Rvu" was said to both of them.

Yehudis, R. Chiya's wife, had an excruciating pregnancy. Afterwards, she disguised herself and asked R. Chiya whether a woman is commanded about Peru u'Rvu. He said that she is not. She drank a sterility potion.

Toras Kohanim (on 22:25): Castration applies to females. We learn from "Mashchasam Bahem Mum Bam";

R. Yehudah says, castration does not apply to females. "Ki Mashchasam Bahem Mum Bam Lo Yeratzu Lachem" teaches that they (castrated animals) are not acceptable Korbanos.

Rishonim

Rif and Rosh (Shabbos 40b and 14:9): "Uv'Artzechem Lo Sa'asu" forbids castrating a person.

Rosh (and Ran DH Ela): Even R. Shimon, who permits Davar she'Eino Miskaven, forbids a man forbidden to drink a potion for jaundice, since it is a Pesik Reishei.

Rambam (Hilchos Isurei Bi'ah 16:11): One who castrates a female person, animal or bird is exempt.

Magid Mishnah: In Toras Kohanim, R. Yehudah says that there is no castration of females. The Rambam explains that there is no Chiyuv for castration of females, but it is forbidden, since Toras Kohanim did not say that it is permitted.

Rebuttal #1 (Gra EH 5:25): The Rambam rules like the first Tana there, who includes castration of females from "Ki Mashchasam". There are no lashes because it is not included in "Lo Sa'asu".

Prishah (EH 5:30): The Lav of castration does not apply to females because they are not commanded about Peru u'Rvu, but there is an Isur due to "Lo Sohu Vera'ah (Lasheves Yetzarah)" (a Mitzvah from Nevi'im to have children).

Rebuttal (#2 of Magid Mishneh, and of Prishah - Taz EH 5:6): 'There is no castration of females' connotes that it is permitted! Rather, since one does an action to castrate her, e.g. he hits or kicks or does some other action that causes sterility, we cannot say that it is permitted. Even regarding animals, it is forbidden due to paining animals, even without the Isur of castration. If the Isur were due to "Lo Sohu Vera'ah", we would not permit through a potion! Rather, it is like I said (the Isur is due to hurting her). One is exempt for a female even through an action, because her reproductive organs are internal, therefore it is not an act of castration even if it is done through an action.

Rambam (12): A woman may drink a potion that sterilizes.

Source (Beis Yosef EH 5 DH v'Asur): The Tosefta (Yevamos 8:2) permits for a woman and forbids for a man. Also the episode with R. Chiya's wife suggests that a woman is permitted.

Tosfos (Shabbos 111a DH bi'Zkenah): Castration after castration does not apply to an (old or sterile) female, for castration does not apply to women.

Poskim

Shulchan Aruch (EH 5:11): One who castrates a female person or animal or bird is exempt.

Shulchan Aruch (12): One may not give to drink to a person or animal or bird a potion to sterilize. One is not lashed for this. A woman may drink such a potion.

Bach (DH v'Ishah): Tosfos says that it is impossible to castrate females (directly. The only way is through a potion.) The Rambam forbids castrating females, but he permits a female to drink a potion! We must say that it is permitted only if she has more labor pain than other women, or for the sake of a cure.

Rebuttal (Taz 7): Tosfos means that there is no Isur to castrate a female. It is possible (directly). The Poskim permit through a potion even if she did not have pain.

Chelkas Mechokek (6): How can the law be more stringent about animals than about women? It is difficult to say that she may drink, but others may not give her to drink. The Bach permits only if she has (excessive) pain in labor. This is difficult, for the Tur did not mention pain at all! Semag permits giving a woman to drink, but not to men or animals. R. Izik Stein explains that we decree male animals due to men. Alternatively, the Torah forbids, like for men. This shows that only male animals are forbidden.

Beis Shmuel (14): The Shulchan Aruch connotes that it is permitted even without pain. The previous Sa'if forbids castrating through an action. The Rambam and Semag hold that castrating through an action is possible (but forbidden).

Gra (28): One is not lashed for casg a female, since "Ma'uch..." (the beginning of the verse "uv'Artzechem Lo Sa'asu") does not apply.

Chasam Sofer (EH 1:20): The Rambam holds that it is possible to castrate women through an action; Tosfos disagrees. Atzei Arazim (20) asked from Kidushin 29a, which says that all Lavim apply to women, except for three. It did not mention castration. Rav Ada bar Ahavah holds that a woman is liable for cutting or shaving the sideburns or beard of a man, and the Mishnah teaches that she is exempt for her own. Likewise, it should teach that she is exempt for castrating herself! Rather, we must say that it is impossible. The Rambam teaches that one is exempt for a female, i.e. an animal. They would remove the wombs of cows and pigs that left Mitzrayim. This is not feasible regarding a woman. However, the Pleisi (Tif'eres Yisrael on Hilchos Nidah) 194:4 proved that it is feasible regarding a woman! How can we explain Kidushin 29a?

Chasam Sofer: How does R. Yehudah learn from "Mashchasam" to exclude females? The verse does not discuss males! Rather, the verse discusses the Ever and testicles, like it says in Bechoros. The Tana'im hold that "Krus" regarding Mumim is the same Krus as regarding Petzu'a Daka. This is clear from Yevamos 75b, that Petzu'a, Krus and Dach apply only to the Ever, Beitzim and strings (from which the Beitzim are suspended). The Torah did not forbid these because they sterilize. The Torah obligates even for castrating one who was already castrated! Rather, it is a Gezeras ha'Kasuv to obligate only for these. I say that one is liable for castrating the male organs of an Androginus (one who has male and female genitals). Even if Eliyahu would tell us that an Androginus is a female, the Torah did not exclude females. It excluded only the female organs. An Androginus may castrate his female organs. Even if Eliyahu would tell us that he is a male, the Torah excluded the female organs. This is why the Mishnah did not say that women are exempt for castration (since it does not apply to their organs). Tosfos does not argue with the Rambam. He means that there is no law of castrating the female organs. The only reason to forbid is due to Peru u'Rvu, according to the opinion that this Mitzvah applies to women. Therefore, it is totally permitted if she is sterile.

Chasam Sofer: The Rambam and most Poskim hold that there is no Isur Torah for a man to drink a potion. If so, for a woman it is permitted l'Chatchilah, even without jaundice or (excessive) pain in birth. The Rambam holds that every Lav in the Torah forbids action, but not Gerama (causing), e.g. erasing Hash-m's name. According to those who permit a Pesik Reishei regarding an Isur mid'Rabanan (see Magen Avraham 314:5), why can't a man drink a potion to cure jaundice. Rashi forbids Gerama mid'Oraisa. He could forbid causing castration to a female (e.g. through a potion) mid'Rabanan. Most Poskim permit it.

Igros Moshe (EH 3:12): A woman gave birth to blemished children, and she wants to be sterilized. I see no Heter, since she is not in danger. The Gra (5:25) holds that the Torah forbids castration of females, just one is not lashed for it. "Uv'Artzechem Lo Sa'asu" does not apply to them. It is a mere Isur due to "Mashchasam". Even if it is only mid'Rabanan, we do not permit all mid'Rabanan laws for a need, unless there is danger. Pischei Teshuvah (10) brings the Birkei Yosef (citing the Ritva), who permits a man to drink a potion if there is danger. The Chidush is the inference, that it is forbidden without danger, even if there is great pain. He proves this from R. Chiya's wife. Had she been commanded about Peru u'Rvu, it would have been forbidden for her to drink it, even though she had great pain in birth.