In a large skillet, cook chorizo and ground beef over medium-high heat until browned, breaking up with a spoon. Add onion and garlic, cooking for 3 more minutes.
Drain excess fat and transfer meat mixture to slow cooker.
Add black beans, pinto beans, diced tomatoes, tomato paste, beef broth, chili powder, cumin, smoked paprika, and salt. Stir well to combine.
Cover and cook on LOW for 6-8 hours or HIGH for 3-4 hours.
Taste and adjust seasonings as needed before serving.
Serve hot with sour cream, fresh cilantro, and lime wedges on the side.