The first: Is the animal a threat to your survival? The second: Is the animal, once dead, going to be a food, weapon, clothing, or shelter source to you? And the third: Is the animal in enough suffering that you would be helping it by killing it? Animal abuse is the worst thing I can think of that would make human survival less worth it. An animal should never be abused, and we should only kill them if the result falls into one or more of the three things I mentioned. Animals are meant to share this world with us. Is it not our duty to protect them?
Never wound what you can't kill. If in animal is in terrible pain and has little to no chance of recovering, then the humane thing to do would be to euthanize it. But under no circumstances is it morally acceptable to abuse or torture animals. Animals can suffer, too and deserve our moral consideration.