Heat a large skillet over medium-high heat. Cook and stir sausage and beef in the hot skillet until browned and crumbly, 7 to 10 minutes; drain and discard grease.

Stir diced tomatoes, onion, tomato paste, vinegar, chili powder, salt, and red pepper flakes into sausage mixture. Fold in cabbage. Reduce heat to medium-low and cook, stirring occasionally, until cabbage is tender, 20 to 25 minutes.