Gemara

(Beraisa): If he slaughtered half the Kaneh, paused the time for a full Shechitah, and completed the Shechitah, it is Kosher.

The Beraisa discusses a bird, and not an animal;

If half is like the majority, it was already slaughtered;

If half is not like the majority, the Shechitah did not yet begin (since the bird can live with a half-cut Kaneh, he may finish cutting. He did not pause during the actual Shechitah.)

Question (Rav Papa): What is the law of Chaladah (Shechitah when the knife is covered) in the minority of the Simanim?

This question is unresolved.

32a - Question (Rav Huna brei d'R. Noson): If he paused while cutting the minority of the Simanim, what is the law?

This is unresolved.

Rishonim

Rambam (Hilchos Shechitah 3:4): If he paused in order to lift the animal and make it lie down, or in order to slaughter only the minority of Simanim, but not for a full Shechitah, this is Safek Neveilah.

Rambam (5): After slaughtering the majority of one Siman in a bird or of both in an animal, even if one delays half the day and later finishes cutting the Simanim it is permitted. Once he slaughtered the majority properly, it is as if he cuts slaughtered meat.

Rosh (2:6): Rashi explains that Rav Papa asked about Chaladah in the latter minority after cutting the majority. This was not resolved, so we are stringent about Chaladah, Hagramah, and Shehiyah in the latter minority. R. Tam challenged this, for a Tosefta is Machshir Shehiyah in the latter minority. Rather, Rav Papa asked about Chaladah in the first minority. Also the question about Shehiyah discusses the first minority. Even though any hole in the Veshet makes Tereifah, perhaps Shehiyah disqualifies only in a matter that makes a Neveilah, e.g. after the majority of the Siman. According to this, if it does not disqualify, mid'Oraisa Shehiyah does not apply to birds, for the majority of one Siman suffices. The Gemara said that the Shi'ur of Shehiyah for a bird is the time to slaughter a bird. I.e. Shehiyah disqualifies mid'Rabanan. This is difficult. A Tosefta disqualifies Shehiyah in the first minority. Why didn't the Gemara bring the Tosefta? If you will say that the Gemara did not know the Tosefta, we can similarly answer for Rashi!

Rosh: The Rambam is Machshir Shehiyah, Derasah, Chaladah, or Hagramah in the latter minority, since he slaughtered the majority properly. Perhaps he relies on the Tosefta that is Machshir regarding Shehiyah, and the same applies to all of them. Rabanan (19a) are Machshir Hagramah in the latter minority. However, we can say that since the Gemara did not resolve the question, we should be stringent, like Rashi. Presumably, the Gemara did not bring the Tosefta to settle the question because it knew that it was not taught in the academy of R. Chiya and R. Oshaya, therefore we do not rely on it. This is better than saying that the Gemara did not know it. Presumably, any Tosefta that became known only after the Gemara was codified is unreliable. Chachmei Yisrael wanted to make a correct, lasting opus, so they investigated to know all the Seforim written of Divrei Chachamim, and selected those that are reliable, and used them to compose Shas. Therefore, we do not rely on the Tosefta. Even though we are Machshir Hagramah in the latter minority, I wrote above that the Rivam distinguished Hagramah from other Pesulim of Shechitah.

Rosh (1:24): The Rivam distinguishes Hagramah from Chaladah and pausing. Regarding the latter two there is a Safek if they occurred after slaughtering half. Regarding Hagramah, we surely follow the majority, since Hagramah is not in the place of Shechitah. It is like cutting the leg after Shechitah. This is reasonable.

Rosh (2:6): R. Oshaya gave the correct explanation. The Gemara discusses Shechitah with a bad knife. If he slaughtered the majority of one Siman in an animal, and cut back and forth on the remaining minority the entire day, what is the law? Perhaps we are Machshir back and forth the entire day when one is engaged in cutting the Simanim. If the majority was already cut, it is as if he cut the entire Siman, and delays to cut the leg (before cutting the other Siman). The question has no connection to the Tosefta. In Ashkenaz and France the custom is to be stringent, like Rashi.

Mordechai (604): Because this was not clarified, and there are opinions about how to explain the question, we should forbid every Shehiyah and Chaladah in the first and last minority of the Kaneh and Veshet, and beware not to delay cutting the latter minority with a bad knife.

Poskim

Shulchan Aruch (YD 23:5): After Shechitah of most of one Siman in a bird, or two in an animal, Shehiyah does not disqualify. Therefore, Shehiyah does not apply to the Kaneh of a bird at all.

Beis Yosef (DH u'Mah she'Chasav v'Hani and DH v'Chasvu): The Tur says that Shehiyah disqualifies in the Kaneh of an animal. According to one explanation (R. Oshaya), this was the question. The Rashba, Rosh and Ran say that R. Oshaya's Perush is correct.

Shulchan Aruch (ibid.): Some say that as long as both Simanim were not totally slaughtered, Shehiyah disqualifies. L'Chatchilah, one should be concerned for this opinion.

Beis Yosef (ibid.): Rashi explains that he asked about Shehiyah after cutting the majority. Do we say that once he cut the majority, it is Kosher? Or, since he later finished, it is one Shechitah?

Beis Yosef (DH veha'Rambam): The Rambam holds that after slaughtering the needed majority (or majorities), Shehiyah, Derasah, or any Pesul of Shechitah does not apply. It is as if he cuts the leg. Therefore, he says (Halachah 7) that Shehiyah does not apply to the Kaneh of a bird at all. If he slaughtered the majority, the Shechitah finished. If he slaughtered the minority, he may resume whenever he wants. It is not forbidden due to Neveilah until the majority is cut. The Rashba and Semag agree. This is only if he knows that he did not touch the Veshet at all, e.g. he was holding the Kaneh alone in his hand. If not, we must be concerned lest he touched the Veshet.

Rema: Even b'Di'eved, the custom is to consider it Tereifah. Therefore, if after slaughtering the majority of both Simanim the animal or bird delays dying, one should hit it on the head to kill it, and not resume slaughtering.

Beis Yosef (DH u'Mah she'Chasav b'Shem): The Tur brings from Rashi (32a DH Teiku) that if after slaughtering the majority of the needed Simanim, it delays dying, it is better to hit it on the head than to resume slaughtering.

Beis Yosef (DH u'Mah she'Chasav Rabeinu): Also Semak, and Hagahos Maimoniyos in the name of Semag, say that the custom is like Rashi. Even if one cut both Simanim, he should not cut off the head afterwards, lest he unknowingly left part of the Simanim uncut (so this is like finishing the Shechitah after a pause in the latter minority). Sefer ha'Terumah says that when hitting it on the head, he should be careful not to break the neckbone. The Mordechai is stringent like all opinions. Where there is no custom, one may rely on the Rambam, who says that after slaughtering the majority, nothing disqualifies. This is reasonable, and a Tosefta explicitly says so.

Shach (12): The Maharshal says that Sefer ha'Terumah is an excessive stringency. Surely, breaking the neckbone with a knife does not look like Shechitah. He understood that Sefer ha'Terumah is stringent due to Shehiyah. This is wrong. Rather, if one breaks the neckbone of an animal before it dies, it is forbidden, for then blood is absorbed in the limbs (113a). L'Chatchilah one may not break the neckbone even if he plans to eat the meat raw (67:3). The Maharshal himself (8:99) rules like this!

Shach (13): The Ratz (Mahariyo Shechitah 15:5) permits to finish the Shechitah afterwards with a blemished knife. This is wrong. Also Semak forbids to finish the Shechitah with a knife or axe, due to Shehiyah. A Stam axe is (not checked for nicks, and presumably is) blemished. In any case it is forbidden due to Ikur (uprooting a Siman) in the latter minority of the Siman. Also the Bach says so.

Pischei Teshuvah (9): A Rav said that if one knows that he totally cut a Siman, he may finish after a total pause. The question of Shehiyah in the latter minority does not apply. Meir Nesivim (17) argued. Even after slaughtering one Siman in a bird, Shehiyah disqualifies.

Pischei Teshuvah (10): A case occurred in which a Shochet cut only the entire Kaneh. The buyer saw that it was still alive. He returned it to the Shochet, who cut the Veshet. Noda bi'Yehudah (2 YD 2) said that one may not rely on Shevus Yakov (2:54), for Shevus Yakov is Machshir only regarding the latter minority, but not when the entire Veshet was not cut. Once, the buyer cut the other Siman with a scissors. A Rav permitted it. The Chasam Sofer (YD 42) forbade, for we do not distinguish the Shochet from anyone else. One could say that cutting with scissors is not called Shechitah, rather, shearing, for it is unlike an axe. In practice, surely one may not rely on this.

Shulchan Aruch (2:10): If a Pasul slaughtered the first half of the one Kaneh, and a Kosher completed the Shechitah, it is Kosher.

Shach (2:29): Even though we hold that any amount of Shehiyah disqualifies, on the Kaneh or Veshet, this law applies if he held the Kaneh alone in his hand (so we know that he did not touch the Veshet). Even we (who are stringent like Rashi) hold that this is Kosher. This is why the Rema did not disagree.