The way I learnt to cut mangoes is as follows:
Stand mango and cut from top down on one side of the seed, and then on the other side of the seed.
You can peel and eat the small amount of mango that remains around the seed. Then cut through the flesh across and down, not pressing too hard so the skin remains uncut.
Then press the middle of the bottom of the mango and the cubes you have created separate.
I just then scoop the cubes out into a bowl and eat with some passion fruit and / or cream, if I have them.
Otherwise you can freeze the cubes if all your mangoes ripen at once.