Gemara

Mishnah: If an animal died (on Yom Tov), one may not move it.

A case occurred, and they asked R. Tarfon about this and Chalah which became Tamei. He asked in the Beis Medrash, and they said not to move them.

Suggestion: Our Mishnah is unlike R. Shimon (the first Tana of the following Mishnah):

(Mishnah): We may cut gourds in front of animals, and a carcass in front of dogs (on Shabbos);

R. Yehudah says, if it was not dead when Shabbos began, we may not cut it,

Rejection: R. Shimon agrees that an animal that died is forbidden.

Question: This is like Mar bar Ameimar, who says that R. Shimon agrees that an animal that died is forbidden. How can we answer for Mar bar Rav Yosef, who says that R. Shimon permits even an animal that died?

Answer (Ze'iri): Our Mishnah discusses a Korban (even the opinion that permits to redeem to feed to dogs does not permit to redeem on Yom Tov).

Support (Mishnah): They asked about this and about Chalah which became Tamei.

Just like Chalah is Kadosh, also the animal!

Inference: A Korban that died is forbidden, but if it was Chulin it would be permitted.

Question: Our Mishnah supports Mar bar Rav Yosef, but it is unlike Mar bar Ameimar, who says that R. Shimon permits even an animal that died!

Answer: All agree to our Mishnah. It discusses an animal that was dangerously sick (from before Yom Tov. If it was Chulin it would be permitted.)

Shabbos 156b (Mishnah): We may cut gourds in front of animals, and a carcass in front of dogs (on Shabbos);

R. Yehudah says, if it was not dead when Shabbos began, we may not cut it, since it was not Muchan.

Levi holds like R. Yehudah. Levi would not look at a Safek Treifah on Yom Tov until they brought it to the wasteheap. He said that if it will be found to be Treifah, they must leave it there. One may not even give it to dogs.

Rishonim

Rif and Rosh (3:8): We establish our Mishnah to discuss a dangerously sick Kodesh animal. If a Chulin animal was dangerously sick, the owner intended before Yom Tov to feed it to dogs, therefore it is permitted.

Hagahos Ashri: This is why we inspect a (Safek) Tereifah near a wasteheap, because if it is Tereifah it is forbidden to move it.

Question (Ba'al ha'Ma'or): The Rif rules like R. Yehudah on Yom Tov, therefore even if it was dangerously sick it is forbidden!

Answer (Ba'al ha'Ma'or): The Rif's text concludes that all agree to our Mishnah. It discusses an animal that was dangerously sick from before Yom Tov. I.e., R. Shimon agrees that the Isur of Muktzah applies to animals, and R. Yehudah agrees that if it was dangerously sick it is permitted, for it is as if it was dead. However, the proper text merely says that our Mishnah discusses a dangerously sick animal, i.e. it is like R. Shimon but R. Yehudah argues. This is like Ze'iri. Rav Nachman says that the Stam Mishnayos about Yom Tov are like R. Yehudah; he would not establish our Mishnah this way. Alternatively, Rav Nachman could agree that the animal was dangerously sick. Even R. Yehudah permits on Yom Tov because everything permitted on Shabbos is permitted on Yom Tov. Rav Nachman said that the Stam Mishnayos about Yom Tov are like R. Yehudah regarding Muktzah special to Yom Tov. An example is a beam that broke that day; no beam may be burned on Shabbos.

Rambam (Hilchos Yom Tov 2:16): If an animal died on Yom Tov, if it was dangerously sick before Yom Tov, one may cut it up for dogs. If not, since he did not intend before Yom Tov (to give it to dogs), it is Muktzah and he may not move it.

Poskim

Shulchan Aruch (497:17): If on Yom Tov an animal was found to be Tereifah after Shechitah, one may not move it, but he may sell it to a Nochri...

Mishnah Berurah (51): Even if it was in the sun one may not move it to the shade. We do not permit lest one not slaughter and refrain from Simchas Yom Tov, for one may move it before Shechitah, or after Shechitah but before checking if it is Tereifah. Some say that one would not refrain from slaughtering because Treifos are uncommon. However, nowadays we are stringent about Treifos of the lungs so Treifos are common, so we allow hiding the carcass in a place where it will not spoil. This does not apply to chickens and geese, for we are not stringent about Treifos of their lungs.

Mishnah Berurah (ibid.): Some say that according to the Rema, who permits Muktzah on Yom Tov, the carcass may be moved. Others say that since it was destined for people (to eat) and now it is destined for dogs it is Nolad, so also the Rema forbids.

Kaf ha'Chayim (102): L'Chatchilah one should check it in a place where it will not need to be moved if it is found to be Tereifah. B'Di'eved, one may move it through a Nochri.

Shulchan Aruch (518:6): If an animal died on Yom Tov one may cut it up for dogs to eat only if it was dangerously sick from before Yom Tov. If it was only sick it is Muktzah, and one may not move it from its place.

Magen Avraham (9): One may cut it up only if it is hard (for dogs to eat it if it is whole).

Question: The Tur says that R. Shimon agrees that an animal that died on Yom Tov is forbidden unless it was sick from before Yom Tov. The Gemara (Shabbos 156b) inferred that Levi holds like R. Yehudah because he inspected Safek Treifos only by the wasteheap!

Answer #1 (Beis Yosef DH Behemah): The Tur must say that the animal was sick before Yom Tov, for otherwise R. Shimon agrees!

Answer #2 (Beis Yosef Sof Siman 497 DH u'Mah she'Chosav): If an animal that was healthy before Yom Tov died on Yom Tov, R. Shimon agrees that it is forbidden for he had no intent for it. But R. Shimon permits an animal found to be Tereifah after Shechitah, for he planned to feed it to dogs if it will be found to be Tereifah.

Mishnah Berurah (33) and Bi'ur Halachah (DH Af Al Pi): The Magen Avraham says that those who permit Muktzah on Yom Tov permit even if it was healthy at the start of Yom Tov. The Graz says that since it was for people and now it is for dogs, it is Nolad, and even the Rema forbids.

Rebuttal (Chazon Ish 43:10): The Rosh cites R. Tam to say that Shmuel forbids Nolad, yet Shmuel rules like R. Shimon regarding an animal that died on Shabbos. Rather, this is not Nolad because one kills an animal in order to use it. We do not distinguish whether or not it died through Shechitah. This is unlike date pits (which are Nolad even though they are normally removed when eating), for that is Panim Chodoshos; they were subordinate to the dates and now they are not.

Bach (DH Behemah): The Ran says that the correct text is like Rashi and the Ba'al ha'Ma'or. R. Yehudah forbids even if the animal was dangerously sick before Yom Tov. Therefore, one should be stringent in all cases.