In a blender, purée the flesh of the limes with the mint, coconut water and sugar until smooth. Strain through a sieve into a pitcher. Cover and refrigerate for 2 hours.
Fill glasses with the ice cubes. Pour in the lemonade. Garnish with mint leaves and slices of dried lime (see recipe). Serve immediately.
Note
For an alcoholic version, add 1 ½ oz (45 ml) white or dark rum per serving.