Cut the fruit off from 1 mango and put it in a blender with the milk, water, sweetened condensed milk. Process until you get a puree. Pour the mango puree into ice cube trays and freeze for at least 3 hours or overnight.
Drop the frozen mango puree cubes in a blender and pulse until you get a coarse crumbs. (Do not process too long, otherwise it will turn mushy)
Scoop the ice into serving bowls and top with the remaining mango fruit pieces. Drizzle a little more sweet condensed milk on top.
It is a good idea to freeze your serving bowls prior to serving. It will keep the shaved ice cold longer. Serve your mango shaved ice immediately. If you desire, top with ice cream and/or whipped cream.