1. Put 1/3 cup each water and sugar in a small saucepan. Bring to a boil and stir until sugar is dissolved. Add 1 sliced lime; simmer 1 minute. Remove from heat and let cool. Strain syrup and reserve.
2. Put syrup and 8 cups diced seedless watermelon in the bowl of a food processor. Process until smooth. Pour into a 13 x 9 x 2-inch baking dish and freeze for 4 hours, stirring thoroughly every hour. When mixture is frozen, place in food processor in batches and pulse a few times. Spoon into serving dishes and garnish with fresh mint, if desired.