Slice both cheeks (sides) from the mango, cutting as close to the flat pit as possible.
Place one cheek skin-side down. Make 5 or 6 deep, vertical cuts into the fruit, but don't slice through the skin. Then make 5 or 6 more cuts crosswise (also without slicing through the skin) to form cubes.
Using a large spoon, and getting as close to the skin as possible, scoop cubes from skin. Slice peel from remaining piece of mango, then slice remaining fruit away from pit and cube.