What magical spell must be cast to turn animal into meat? Isn't it already meat just wearing a fur coat?

It's a magical spell cast with a very sharp knife, and involves a grisly process of removing all material typically considered inedible.

I think you'd at the very least separate the fur coat from the meat. Tarrare seemingly ate every part of the cat except for the bones - and then just vomited out the extra bits (like the fur coat).