In a small saucepan, mix the mint leaves, water, and sugar. While stirring, bring to a boil until the sugar dissolves. For one minute, simmer. Remove syrup from the heat and allow it to soak for 30 minutes or so.
Along the mango seed, cut the sides. Without cutting through the mango peel, slice the flesh in a grid-like pattern. To separate the flesh from the skin and remove the cubes, use a large spoon.
In a blender or food processor, add the mango flesh and water, and pulse until smooth. If necessary, add more water to achieve the required consistency.
Place the optional sugar syrup in a jar after the mango juice. This is entirely optional, so you can add however much or how little sugar syrup you like. To blend, stir.
Garnish with mint leaves and serve with ice cubes.