Behavior
The Butcher's primary job is to collect animals from a rancher pen, bring them back to the Butcher structure, and slaughter them for meat for the village.
Leading Animals
The Butcher will randomly choose an available Animal pen and attach a lead to an animal in that pen if it is at least 75% full. For rules on what makes a full pen, see the Rancher Pen. The animal that gets chosen from the pen is mostly random, but the butcher will try to prioritize taking non-villager animals.
Once the animal is attached to the lead, the butcher will escort it over to the butcher structure. While being lead the animal gets a small speed boost to keep up and the ability to teleport if they get stuck.
Slaughtering Animals
Using his axe, the Butcher harvests the animals that are in the Butcher Structure into meat and other by-products as per vanilla drops. Villager animals produce villager items; non-villager animals do not.
The Butcher receives 1 to 3 extra pieces of meat from butchering animals based on their skill level and the quality of axe they are using at the time.
Crafting
The Butcher can utilize a crafting bench placed inside the Butcher structure to do some craft. If enough leather has been acquired, all four pieces of leather armor can be crafted per the vanilla recipes. This armor will be brought to storage and equipped by a Guard or you may sell it to the Merchant.
Eventually the Butcher's axe will break. When it does the Butcher is capable of crafting his own wooden axe at the crafting table in his structure. Obviously an iron or diamond axe crafted by the Blacksmith would be more effective and yield much better results.