Combine grapefruit drink and sugar in a bowl until sugar is dissolved. Stir in Aperol.
Chill in refrigerator for 2-3 hours.
Churn the mixture in an ice cream machine according to the manufacturer's directions.
Add to an airtight container and freeze for at least 2 hours until hardened.
An hour before serving, create shavings using a fork or spoon to scrape at the hardened ice. Place back in the freezer for one hour to re-harden.
Serve in glasses or hollowed-out grapefruit skins. Garnish with a mint sprig, a grapefruit slice, or a grated citrus zest sprinkle.