Combine sugar and water in a small saucepan.
Bring to a boil; cook over medium heat until sugar dissolves, stirring constantly.
Boil 5 minutes without stirring.
Remove from heat, and let cool slightly.
Combine sugar mixture, grapefruit juice, and grenadine syrup; stir well.
Cover and chill thoroughly.
Pour mixture into freezer can of a 2-quart hand-turned or electric freezer.
Freeze according to manufacturer's instructions.
Letripen 1 hour, if desired.
Scoop into individual dessert bowls.
Garnish with fresh mint sprigs, if desired.