In a small saucepan combine the sugar and 1 cup water, bring the mixture to a boil, stirring until the sugar is dissolved, and remove the pan from the heat. Let the syrup cool. In a blender puree the mint with the syrup, stir in the lime juice, and in a bowl chill the mixture, covered, for 1 hour, or until it is cold. Freeze the mixture in an ice-cream freezer according to the manufacturer's instructions.