Beitzah, Chapter 3, Mishnah 5. The Mishnah opens: "Behemah shemesah" - an animal that died on Yom Tov, "lo yezizenah mimkomah" - may not be moved from its place, because it is muktzeh.
Which animal is the Mishnah discussing:
The Gemara explains that the animal in our Mishnah was a consecrated animal, that is, a korban. Since it died without having been properly slaughtered, it became entirely forbidden to derive any benefit from it and it must be buried, and for that reason it may not be moved at all.
With an ordinary, non-consecrated animal that died on Yom Tov, however, we must distinguish between two situations:
It was already dangerously ill before Yom Tov: If it was already failing before Yom Tov, and while it was still daytime it was clear that it was likely to die on Yom Tov, one may cut it up and feed it to his dogs on Yom Tov, since already from the previous day he had it in mind that it would end up going to the dogs.
It was not dangerously ill before Yom Tov: Even though it is an ordinary animal, moving it is forbidden.
The incident with Rabbi Tarfon:
The Mishnah continues: "Uma'aseh shesha'alu es Rabbi Tarfon aleha ve'al hachallah shenitmeis" - Rabbi Tarfon was asked about two cases: about the consecrated animal that died on Yom Tov, and about challah that had been separated from the dough in order to be given to a kohen and then became tamei, so that it is no longer fit to be eaten.
"Venichnas leveis hamidrash vesha'al" - Rabbi Tarfon went into the beis midrash and asked what the halachah is in these two cases. "Ve'amru lo: lo yezizem mimkomam" - the Sages answered him that they may not be moved from their place, since both are muktzeh and forbidden to be handled on Yom Tov.
In summary: In this Mishnah we learned that a consecrated animal that died on Yom Tov may not be moved, because it is forbidden to derive benefit from it and it must be buried; with an ordinary animal, everything depends on whether it was dangerously ill before Yom Tov, and only then may one cut it up and feed it to the dogs. We also learned from the incident with Rabbi Tarfon, who asked in the beis midrash about the animal and about the challah that became tamei, and was told that in both cases they may not be moved from their place because of muktzeh.