Gemara

(Mishnah - R. Yishmael): If the day of the Omer (Nisan 16) is Shabbos, the Isaron is sifted from three Sa'im (of barley). On a weekday, it is sifted from five Sa'im.

Chachamim say, whether or not it is Shabbos, it is sifted from three Sa'im.

R. Chanina Segan ha'Kohanim says, on Shabbos one person reaps it using one sickle and one box. On a weekday three people reap it. Each uses his own sickle and his own box;

Chachamim say, whether or not it is Shabbos, three people reap it, each with his own sickle and box.

64a (Rabah): R. Yishmael and R. Chanina Segan ha'Kohanim agree with each other;

R. Chanina forbids unnecessary exertion on Shabbos. Presumably, he forbids also unnecessary reaping on Shabbos!

(Rava): If two figs are needed to save Shimon's life, and one finds two isolated figs, and one branch with three figs, he should take the branch. R. Yishmael forbids reaping a larger quantity only when it entails more acts of reaping. Here, reaping a larger quantity entails less acts!

Shabbos 133b (Beraisa): (On Shabbos,) as long as one is circumcising, he may cut strands whether or not they are Me'akev (invalidate the Milah). Once he removes his hand, he may go back to cut strands only if they are Me'akev.

Question: Who is the Tana of the Beraisa, who forbids going back to cut strands that are not are Me'akev?

Answer #1 (Rabah bar bar Chanah): It is R. Yishmael, son of R. Yochanan ben Brokah;

(Beraisa - R. Yishmael): If Erev Pesach is on Shabbos, we flay Korban Pesach until the chest (then stop to remove and deal with the Eimurim). We flay the rest at night;

Chachamim say, it is flayed entirely on Shabbos.

Rejection: R. Yishmael does not allow flaying it entirely because "Zeh Keli v'Anvehu" (beautifying Mitzvos) does not apply (after the Eimurim were removed). It applies to the Mitzvah of Milah, so he would permit non-essential strands!

(Beraisa): We cut strands (that are Me'akev). If not, he is Chayav Kares.

(Rav Kahana): The Mohel is Chayav Kares.

Objection (Rav Papa): He can say 'I did half the job. You (others) can finish!'

Answer (Rav Ashi): The case is, he began to circumcise at the very end of Shabbos. He was warned that he would not have enough time to circumcise fully, and even so, he began. He is Chayav Kares for wounding (without fulfilling the Mitzvah).

Rishonim

Rashi (133b DH Neima): Rav Papa asked that the Mohel can say 'I did half the job. You can finish!' I.e. he was permitted to start. He had Reshus to wound. Why is he Chayav Kares?!

Beis Yosef (Sof Siman YD 262): This implies that he is not Chayav Kares, but there is an Isur, since he did not finish the Mitzvah! Therefore, One should be careful that two Mohelim not do one circumcision l'Chatchilah on Shabbos, e.g. to stipulate that one will Mal (cut the foreskin), and the other will be Pore'a (pull back the skin). Rather, the Mal is also Pore'a.

Rebuttal (Bach DH ha'Beis): The Gemara said that there is no Chiyuv (but there is an Isur) when the Mitzvah was not finished. If another Mohel finished the Mitzvah, no Isur was done at all! It seems that this shows that two may circumcise l'Chatchilah. If not, he could not say 'I did half the job...' We would force him to do the remaining half, to avoid the Isur (of doing only half)! This shows that there is no Isur to do half when someone else finished. Great congregations have the custom to permit this.

Tosfos (64a DH Shtayim): Rava could not settle his question from the Beraisa (Beitzah 17a) that permits filling a pot and cooking it on Yom Tov, even though one does not need so much. Yom Tov is lenient. One may not learn to Shabbos, which is not Nidcheh. A case occurred in which the hot water prepared for a Milah spilled. They warmed up water for the mother (who was still dangerously sick), and added extra for the Milah (Eruvin 68a). The Isur to add (to the amount she needed) is only mid'Rabanan, and Chachamim did not decree when this would postpone Milah, which overrides Shabbos.

Poskim

Shulchan Aruch (YD 266:14): One should be careful that two Mohelim not do one circumcision on Shabbos, i.e. one is Mal, and the other is Pore'a. Rather, the one who cuts, he himself is Pore'a.

Rema: I did not find a proof for this. It seems that it is permitted, for Milah overrides Shabbos, just like Avodah in the Mikdash. Many Kohanim served and were Mechalel Shabbos. Since Avodah overrides Shabbos, it is like a weekday in every way. Sefer ha'Terumah explicitly permits at the end of Hilchos Shabbos. However, I found in a Kovetz that one should forbid. Therefore, l'Chatchilah it is good to be stringent, even though letter of the law it seems like I wrote.

Bedek ha'Bayis: Orchos Chayim writes in the name of Sefer ha'Terumah that two Mohelim may do one circumcision on Shabbos, i.e. one is Mal, and the other is Pore'a. The first is not liable at all, for the second finishes the Mitzvah, like Rav Papa said.

Teshuvas Rema (76): The Beis Yosef's Diyuk from Rashi is invalid. Rashi cited the Beraisa. Also, even if we would say that there is an Isur, that is because the Mohel who stopped in the middle did not know that others will finish. Therefore, it was Asur not to finish the Mitzvah. Therefore, Rav Papa asked why he is Chayav Kares. However, if a Mohel stops in order to let another finished, this is permitted l'Chatchilah. Surely the second Mohel is permitted. He did the primary Mitzvah, since Milah without Pri'ah is as if he was not Mal (137a). The Mitzvah is attributed to the one who finishes. Surely, the first Mohel could not tell others to do an Isur! Rather, even the first is permitted. If he were forbidden, Rav Papa would have no source to distinguish (and say that it is Asur, but without Kares) and challenge Rav Kahana. Perhaps he is liable, for he did not finish! Even though Rashi said 'since he began with Reshus, why is he liable?', perhaps the Beraisa discusses when he had no Reshus, e.g. he did not know how to finish it, and people told him so, and he said 'I will finish', and he did not, like Rav Ashi's answer about one who began close to dark. We must say that we discuss one who did not know how to finish. If not, even without saying 'you can finish', he is exempt because he began with intent to finish! He is not liable retroactively for not finishing. If he were, he would be liable even when he told them 'you finish', and they did not. If so, the question returns!

Note: Perhaps the Beraisa discusses one who said that he does not intend to finish!

Rema (ibid.): Rather, since there are other Mohelim there, it is called that he began with Reshus. I say that it is better through two Mohelim, in order that neither will do a full Melachah. This is like two who did a Melachah; they are exempt.

Hagahah: Sha'agas Aryeh 59 disagreed. Since one may circumcise through one Chilul, it is forbidden through two. Therefore, once one begins to circumcise, he may not remove his hands (cease circumcising) until he finishes Pri'ah. If he stopped, it does not matter whether he or another finishes, for in any case there are two Chilulim. Shabbos and Yom Tov are the same regarding this. Gedolim of Eretz Yisrael ruled to permit, like the Rema, unlike the Sha'agas Aryeh, and they did so in practice. Noda bi'Yehudah (2 OC 22) says that in Polin, they always use two Mohelim, both on Shabbos and on weekdays.

Rema (ibid.): This is like one who uproots (a stationary object), and the other puts to rest (in Reshus ha'Rabim). Here it is permitted in every case. Since Milah overrides Shabbos, it is like a weekday, like it is regarding Piku'ach Nefesh.

Question: In Menachos¸ Rabah said that R. Yishmael and R. Chanina agree with each other. R. Chanina forbids unnecessary exertion (i.e. more reapers) on Shabbos. Likewise, he forbids reaping more than necessary! I.e. the Gemara equates additional people to additional Melachah. Rava said that it is better to cut one branch with three figs, than to detach two figs. This is only because he reaps less. Presumably, he would forbid cutting two branches with a total of three. If not, he should have taught this is Chidush! Likewise, using two people is forbidden when one can do it. Tosfos (64a) connotes similarly. However, Tosfos said only that one cannot learn from Yom Tov, but perhaps really, it is permitted also on Shabbos. Tosfos concludes that one may do extra Melachah for the sake of Milah. Likewise, one may use more people. Perhaps one may cut even two branches with three figs. Rava discussed one branch, for initially he was unsure even in that case. Only R. Yishmael forbids reaping too much, but Chachamim permit. Later I saw that Sefer ha'Terumah permits a Bris through two Mohalim. He proved this from Rav Papa, and from the Tamid. (The Avodah is divided among many Kohanim, even on Shabbos, even though one could offer all of it.)

Levush: There is no source to stringent. It is normal for one to to the entire Milah. One who did half transgressed b'Shogeg. He could have cut all of it in one cut. If one could circumcise through one cut, and he circumcised through many small cuts, surely he is liable! However, one cannot of Milah and Pri'ah at once. Therefore, just like one Mohel may do them in two cuts, l'Chatchilah two Mohalim may each do one of them. Since the Beis Yosef was stringent, and the Rema agreed, I do not counsel people to do so, but we do not protest against people who do so.

Question (Taz 11): If there is any reason to forbid (doing half the Milah), perhaps that reason suffices to obligate Kares! What would be Rav Papa's source to distinguish (to say that it is Asur without Kares) and challenge Rav Kahana?! Rather, there is no Isur at all. Rashi said 'why is he Chayav?' because the Beraisa said that he is liable.

Gra (25): Seemingly, one cannot learn from Avodah on Shabbos, which is permitted. It seems that Milah is merely Docheh Shabbos, like Piku'ach Nefesh. However, this is wrong. Rabah said that R. Yishmael and R. Chanina agree with each other. In Shabbos, we say that R. Yishmael is the Tana who forbids going back to cut strands that are not are Me'akev, but Chachamim would permit. If Milah is merely Docheh Shabbos, all should forbid! Rather, it is no different (than Avodah). Just like Chachamim permit using three people on Shabbos, just like on a weekday, many may do Milah. This is why l'Chatchilah, the Mohel can say 'I will do half...'