How can I butcher non-tame animals that I've captured, like deer in cages?
Non-tame animals are bugged in 31.12 such that if they need to be moved more than a few steps, the dwarves carrying them panic, drop them, and flee, freeing the wild animal (or goblin) and causing chaos.
In addition to this, I believe the "slaughter an animal" task only applies to tame animals. "butcher a dead animal" is how you handle hunted animals, but this is hard given the abovementioned bug.
a) -- throw the animals into a pit. The pit must be as close to the cage with the animal as possible. once you have successfully "pitted" the animal, your marksdwarves / hunters can dispatch it at their leisure.
b) -- build the cage into a room, link it to a lever, station your military, and have someone pull the lever. Military will kill the animal, and then your butcher will run over and grab the corpse.