In a medium pot of boiling, salted water, cook the sweet potatoes until almost tender, about 4 minutes. Drain and set aside.
In a large nonstick skillet, cook the sausage over medium heat until browned and crumbly, about 10 minutes; transfer with a slotted spoon to paper towels to drain.
Heat the oil in the skillet over medium-high heat. Add the bell peppers, onion and garlic and cook until softened, about 5 minutes. Add the sausage, cumin and sweet potatoes and cook for 5 minutes more. Season to taste with salt and pepper and serve with green salsa.