Heat a large skillet over medium-high heat. Cook and stir ground beef and Italian sausage in the hot skillet until crumbly and browned, about 10 minutes. Drain.
Combine ground meats, marinara sauce, tomatoes, and mushrooms in a slow cooker. Cover and cook on Low for 7 to 8 hours.
Stir tortellini into marinara meat sauce. Sprinkle with mozzarella and Cheddar cheese. Cover and cook on Low until tortellini is tender, about 15 more minutes.
