Combine barbeque sauce, mushrooms, tomatoes, onion, brown sugar, garlic, vinegar, salt, and black pepper in a food processor or blender; pulse until mixture is blended but still chunky. If the mixture is too thick, add water.
Arrange pork chops in a baking dish and cover with barbeque sauce mixture; cover with aluminum foil.
Bake in the preheated oven until pork is very tender, about 3 hours. Shred pork with 2 forks.