Mangoes have a pit in the center, so you’ll need to avoid that when cutting. Cut on either side of center, leaving about 1 – 1 1/2″ thick for the pit, as shown in the first picture.
With each half, score the mango down to the skin, but not through the skin, as shown in the second picture.
Flip the mango half “inside out,” as shown in the third picture. With your thumb, release the mango cubes from the skin.
With the pit section, cut the peel off, by running your knife just on the inside of it. Then, carefully slice off pieces around the pit.