Bring a large pot of salted water to a boil. Add potatoes and cook until tender but still firm, 12 to 15 minutes. Drain and set aside.
Heat oil in a large skillet over medium heat. Crumble sausage into skillet and cook, stirring frequently, until browned and no longer pink, about 7 minutes. Remove sausage with slotted spoon and drain on paper towels.
Pour off all but 1 tablespoon oil from the skillet. Heat oil over medium heat and add bell peppers, onion and garlic and cook until softened, about 7 minutes.
Add to the skillet the potatoes, sausage, salsa and cumin. Stir and cook about 5 minutes to heat through and blend flavors. Season with salt and pepper.