In a large skillet, cook beef over medium heat until no longer pink; drain. Stir in the beans, onion, 1/2 cup tomato sauce, chili powder, garlic and cumin.
Spoon about 1/3 cup of beef mixture off-center on each tortilla. Fold edge nearest filling up and over to cover. Fold in both sides and roll up. Fasten with toothpicks. In a large saucepan, combine the chilies, peppers and remaining tomato sauce; heat through.
In an electric skillet or deep-fat fryer, heat 1 in. of oil to 375°. Fry the chimichangas for 1-1/2 to 2 minutes on each side or until browned. Drain on paper towels. Sprinkle with cheese. Serve with sauce.