I know two other methods that I'll share with you. The first one is my favorite. This brings back memories of a day that I picked up some hitchhikers out in the Puna District on the Big Island of Hawaii. We picked a couple of bags of mangos from trees by the side of the road, then went to a local water spigot so we were prepared to wash up after gorging ourselves on luscious, ripe mangos!! 

First, slice each side of the mango along the seed to give two halves.  Then hold one portion of the mango with the peel side down.  Score the fruit down to the peel in a tic-tac-toe fashion. With both hands, bend the peel backwards. Cut the cubes along the peel to remove from the skin.  Remove the remaining fruit on the seed by cutting along the seed.

And another way to prepare a mango:

Cut off both ends of the fruit.  Place fruit on flat end and cut away peel from top to bottom along curvature of the fruit.  Cut fruit into slices by carving lengthwise along the pit.

No matter how you slice it, life is better if you eat more mangos!  Enjoy!