Combine sugar and water in a medium saucepan, and stir well. Bring to a boil, and cook 1 minute or until sugar dissolves, stirring constantly. Let sugar syrup cool completely.
Combine cranberries and juices in a food processor, and process until pureed. Combine pureed mixture and cooled sugar syrup in a 13 x 9-inch baking dish; stir well. Cover and freeze at least 8 hours or until firm.
Remove mixture from freezer; scrape entire mixture with the tines of a fork until fluffy. Serve in Almond Cookie Cups. Garnish with mint sprigs, if desired.