1. Cook sugar and 1 cup water, stirring constantly, in a small saucepan over low heat until sugar has dissolved. Add mint. Bring to a boil. Cook 5 minutes. Remove from heat. Cover; let stand 20 minutes.

2. Working in batches, puree watermelon in a blender. Pour through a fine sieve into a large bowl; discard solids.

3. Pour mint syrup through a fine sieve into a bowl; discard mint. Stir syrup into puree. Stir in lime juice. Refrigerate, covered, at least 2 hours (up to overnight).

4. Freeze in an ice cream maker according to manufacturer's instructions. Transfer to an airtight container; freeze at least 1 hour (up to 4 days). Let stand at room temperature 10 minutes before serving.