Combine the sugar and water in a small pot. Bring to a slow boil over medium heat, and reduce to a simmer. Simmer, uncovered, for about 5 minutes. Remove from the heat and allow to cool for about 10 minutes. Stir in the grapefruit juice and elderflower liqueur and pour into an 8 x 8-inch freezer-safe dish. Transfer to the freezer and mix with a fork every 30 minutes until all the liquid has frozen, about 2 hours total.
Serve in small tumblers with sprigs of mint or slices of grapefruit to garnish.
Store-bought grapefruit juice works just fine.