In saucepan, combine grapefruit juice and sugar. Bruise mint leaves between fingers and add to saucepan. Bring mixture to just boiling, stirring to dissolve sugar. Remove from heat, cover and let stand 5 minutes. Remove mint leaves.

Pour grapefruit mixture into ice cube trays; freeze. Just before serving, place a single layer of frozen cubes in food processor fitted with steel blade. Pulse 12 times or until no large chunks of ice remain. Spoon granita into stemmed glasses. Garnish with grapefruit slice. Repeat with remaining cubes. Serve immediately.