Bring sugar and water to a boil in a small saucepan. Remove from heat, and add mint leaves. Let steep 10 minutes. Strain through a fine sieve into a small bowl, and discard mint. Let cool.
Using a vegetable peeler, remove zest from grapefruit in long, wide strips. Place in a large glass, and add rum. Cover, and let stand for 30 minutes. Strain through a fine sieve into a large glass measure, and discard zest.
Cut away remaining pith from grapefruit. Cut between membranes to release segments. For each drink, place 2 to 3 segments in a glass. Top with 3/4 cup ice. Stir 3 tablespoons infused rum, 2 tablespoons mint syrup, and 1/4 cup seltzer in a glass measure, and pour over ice. Garnish with mint sprigs.