Cut peel and white pith from grapefruits and oranges. Cut between membranes to release segments. Combine fruit in large shallow bowl. (Fruit can be segmented 1
day ahead. Cover and refrigerate.)
Place mint and sugar in processor. Using on/off turns, blend until mint is finely chopped, occasionally scraping down sides of the bowl. Sprinkle mint sugar and dried cranberries over fruit; serve.