WOW! There sure are a lot of funnies that come to mind about this but suffice it to say woodchucks are tough. About the only way really is to either par boil or pressure cook the critter. Separate into pieces removing any vestiges of fat, then cook as above until you can separate meat from bones, discard broth and bones.
Use meat and prepare a soup or stew using any receipe you like. If you have a pressure cooker, cube 2 large potatoes, 1 large white onion, 2 carrots, 2 celery stalks. Add 1 can diced tomatoes, 1 16 oz can beef broth + 1 can water, 1 bay leaf, salt & pepper to taste. Pressure about 12 mins or until potatoes are done. Enjoy!
P.S. How much wood would a woodchuck chuck if a woodchuck could chuck wood?