Because the flesh clings to the large, flat seed in the center of a mango, the easiest way to remove the seed is to carve around it. Stand the fruit stem side up and with the narrow side facing you. Using a sharp knife, cut the mango just to one side of the flat seed, cutting from top to bottom. Repeat on the other side of the seed. Set the two larger cut pieces aside. For the portion with the mango seed, use a knife to cut off the peel and carve off as much of the flesh from the seed as possible. Discard the seed. Another option is to purchase a mango pitter, a gadget that cuts down both sides of the mango seed at once.
The flesh of a mango also clings tightly to the skin. A simple way to remove the flesh is to cube it with a knife and cut the cubes away from the skin. Starting with one of the seedless pieces, place it on a cutting board. Using a butter knife or paring knife, cut the flesh into a crisscross grid of cubes just to, but not through, the skin. Gently cut under each cube to release it from the skin. Use the mango cubes as desired.
When you need slices instead of cubes, use the same method as for cubing, except cut the flesh into slices just to the peel and cut them out as described for the cubes. However, you may find it easier to just cut each seedless portion into individual slices and peel each slice with a vegetable peeler or knife.