If traps for wild animals, birds or fish were set before yom tov, one may not remove captured animals from them on yom tov unless it is known that the animals were trapped before yom tov began. A non-Jew once brought fish to Rabban Gamliel on yom tov. (He did not accept them.) Rabban Gamliel explained that the fish were permitted, he just didn’t happen to want them.
An animal in danger of dying may not be slaughtered on yom tov unless there is enough time left in the day that one could eat an olive-sized portion of its meat roasted. Rabbi Akiva says that even enough time for an olive-sized portion of meat to be taken raw from the neck where it is slaughtered would be sufficient. If one slaughtered the animal in the field, he may not carry it back on a pole. Rather, he must carry it back piece by piece in his hands.