Remove and discard rind and seeds from melon and cut enough fruit into 1/2-inch cubes to measure 2 1/2 cups. In a blender puree all ingredients until smooth. Chill puree, covered, until cold, at least 1 hour, and up to 6. Freeze puree in an ice-cream maker. Transfer sorbet to an airtight container and put in freezer to harden.
Chop mint. In a saucepan bring sugar, water and mint to a boil, stirring until sugar is dissolved. Simmer syrup, undisturbed, 2 minutes. Pour syrup through a fine sieve, pressing hard on solids, and cool. Syrup keeps, covered and chilled, 2 weeks.