With a potato masher or fork, mash together beans, olive oil, cumin, chili powder, and salt in a medium bowl.
Spread 2 tablespoons bean mixture on each tortilla halfway between the center and bottom edge. Top with 1 to 2 tablespoons each diced tomato and cheese; cover with a lettuce leaf.
Fold sides of tortilla over filling; roll from bottom to form a cylinder. Roll in waxed paper and fold ends over; tape to secure. Cut wraps in half diagonally. Serve with avocado and mango, if desired.