Heat 2 teaspoons olive oil in a small saucepan over medium heat. Add onion; cook and stir until slightly translucent, about 3 minutes. Add mushrooms; cook until slightly tender, about 3 minutes. Stir in sazon seasoning. Reduce heat to low and and simmer until flavors combine, about 3 minutes.
Stir ground beef into the saucepan; cook over medium heat, stirring frequently, until crumbly and no longer pink, about 5 minutes. Add tomato puree; reduce heat, cover, and simmer sauce, about 10 minutes.
Slice sweet potato into noodles using the thin julienne blade on a mandoline.
Fill a pot with water; add 1 teaspoon olive oil and a pinch of salt. Bring to a gentle boil. Add sweet potato noodles and cook, 1 to 2 minutes. Remove from water and drain.
Transfer sweet potato noodles to serving plates. Sprinkle feta cheese on top. Cover with sauce. Season with salt and black pepper.