If you find an animal on Yom Tov in a trap that was set up before Yom Tov, it cannot be used since maybe it was caught on Yom Tov.

There was a non-Jew who brought fish to R’ Gamlial on Yom Tov and he said, ‘It is permitted but I do not want to benefit from it’.

Beitzah 3:3

If an animal is dying you should not slaughter it unless you would have the time to eat a portion the size of an olive of meat that is roasted. R’ Akiva says this is true, even if you have time to eat a portion the size of an olive of meat that is raw.

If you slaughter an animal in the field, you should not bring it home on a pole but rather in your hands limb by limb.