Place the venison and sausage in a large skillet and cook, breaking up with a wooden spoon as necessary, over medium heat until no longer pink and evenly browned. Drain grease. Stir in the onions and garlic, and cook until aromatic, about 3 minutes. Drain, and mix in the tomato paste. Season to taste with hot pepper sauce, salt, and pepper.
Pour the cannellini beans and tomatoes into a slow cooker. Stir in the venison mixture. Cover, and cook 8 to 10 hours on Low, or 5 hours on High. Sprinkle each serving with shredded Cheddar cheese.