Peel and section grapefruit over a bowl; squeeze membranes to extract juice. Set sections aside; reserve juice and add water to equal 1 1/4 cups.
Combine juice mixture, prunes, figs, sugar, cloves, and cinnamon in a medium saucepan; bring to a boil. Reduce heat; simmer 15 minutes, stirring occasionally. Remove from heat; let cool. Discard cloves and cinnamon stick. Stir in grapefruit sections and grapes.