It should also be remembered that when trying to understand an animal's pain from a human perspective that a deer or any other animal has no sense of time or future events. Its not like a deer
understands that he is going to die or that he is going to be permanently injured and the animals around them don't know it either. Pain for human means having the ability or curse to imagine the future and know that it will continue and thus changes the entire concept. Imagine root canal or the worst possible toothache you can imagine and realize animals exist with pains much worse( teeth, parasites) without any alteration to their general behavior. The problem for humans is that they know that pain will keep going on and on and that is the real problem and why humans can suffer unlike any other creature and shouldn't even be compared. Still, only an absolute sicko/atheist would do anything but their best
to insure a humane kill since only such persons would have no motive to do so.