A taxidermist is someone that prepares and stuffs dead animals for display. A buffet dinner is a type of dinner where people self serve the food they want to have for dinner. After dinner, people tend to feel really full. Another expression for feeling really full is feeling stuffed. This joke is playing on the wrod "stuffed" and its different meanings. 
I went to a buffet dinner with my neighbor , who is a taxidermist . After such a big meal , I was stuffed .