On a work surface, remove peel and pith from grapefruit using a sharp paring knife, beginning at the top and following the curves of the fruit. Working over a medium bowl to catch the juice, carefully cut between membranes to remove segments. Squeeze remaining membrane to extract juice, reserving for another use; discard membrane.
Divide fruit segments equally between 4 chilled dessert plates. Drizzle 1 tablespoon liqueur over each, and chill until ready to serve.
Just before serving, sprinkle with sliced mint leaves and garnish with a mint sprig.