In a large pot over medium heat, heat oil. Add onion and bell pepper and cook until soft, 5 minutes. Add garlic and cook until fragrant, 1 minute more, then add tomato paste and stir until well coated. Add sausage and cook, breaking up meat with a wooden spoon until no longer pink, 7 minutes. Add chili powder, oregano, garlic powder, and cayenne and season with salt and pepper.
Add sweet potatoes, broth, and tomatoes and bring to a boil. Reduce heat and let simmer, covered, until sweet potatoes are tender, about 15 minutes.