I recently got a dog from the SPCA, a 40lb super mutt (no one can even guess at his origins) named Cooper, and he didn't seem like much of a hunter. He likes to sniff wild animals, no chasing or raised hair. So we had a problem with groundhogs burrowing under our shed. One day I hear rustling in the woods, and out comes Cooper holding a 35lb groundhog (big sucker) by its broken neck. After much praise and treats and chest pounding by me. I dug a 3 foot hole and burried him in the back yard.
P.S. Those gangster films aren't kidding, burying the groundhog was an hour of backbreaking labor, never kill a human in the hopes of burying them somewhere without help of a big burly friend.