Preheat the oven to 350 degrees F (175 degrees C).
Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add sweet potato, cover, and steam until tender, 2 to 6 minutes.
Heat olive oil in a skillet over medium heat. Add onion; cook and stir until translucent, about 5 minutes. Add garlic; cook and stir until fragrant, 2 to 4 minutes. Add the steamed sweet potato, black beans, green bell pepper, spinach, lime juice, cumin, cayenne pepper, and salt. Cook until flavors blend, about 5 minutes. Add 2 cups enchilada sauce; cook until slightly absorbed, about 5 minutes more.
Spoon 1 to 2 cups enchilada mixture into the bottom of a 9x13-inch baking dish and about 1 cup into each tortilla. Arrange filled tortillas in the baking dish. Pour remaining 1 cup enchilada sauce over the tortillas.
Bake in the preheated oven until sauce is deep red and enchiladas are heated through, about 20 minutes.