Peel the mango and cut the pulp from the stone. Finely dice the pulp, place on a flat pan or dish, and place in the freezer for 30 minutes.
Halve the grapefruit and the lime and squeeze the juice.
Peel and coarsely chop the ginger.
Puree the mango, grapefruit juice, lime juice, and ice cubes in a blender. Add the honey to the puree. Pass the ginger through a garlic press into the puree. Puree again briefly.
Pour the smoothie into two glasses, then fill to taste with the chilled mineral water. Stir until combined, garnish with the lime wedges and mint, and serve.