Combine 1 cup cranberry-apple juice drink and sugar in a 2-qt. saucepan. Cook over medium heat until sugar dissolves. Remove from heat and cool completely.
Combine cran-syrup, remaining 2 cups juice drink, and ginger ale. Pour into 3 ice cube trays, and freeze 1 1/2 hours or until almost frozen. Transfer cubes to a blender or food processor, and pulse until slushy.
Pour slush into a 13" x 9" pan, and freeze 3 1/2 hours or until frozen.
To serve, scrape granita in pan with tines of a fork until fluffy. Spoon into dessert glasses, and serve immediately.
*Natural ginger ale has an intense gingery taste. Find it on the soft drink aisle or with beers, especially in upscale markets.