Place black beans, pinto beans, and kidney beans in a large container and cover with several inches of cool water; let stand for at least 12 hours. Bring beans and water to a boil in a large pot; cook until beans are tender and heated through, 30 minutes. Remove pot from heat to cool and drain beans.
Cook and stir sausage, beef, onion, bell pepper, and garlic in a large skillet over medium-high heat until meat is browned, 5 to 10 minutes. Drain and discard fat.
Stir beans, sausage mixture, corn, salsa, chili sauce, vinegar, and water together in a slow cooker.
Cook on High for at least 4 hours, stirring occasionally. Season with salt and ground black pepper.