Bring sugar and 1 cup water to a boil in a saucepan. Add mint; cover and let stand 5 minutes. Pour through a fine wire-mesh strainer into an 8-cup container; discard mint. Add grapefruit juice.
Divide mixture into 2 (1-quart) freezer containers; cover and freeze at least 4 hours. Let stand 30 minutes before serving. Scrape with a spatula, or process, in batches, in a food processor. Garnish, if desired.