Whisk the cranberry juice and sugar in a heavy medium saucepan over medium heat just until the sugar dissolves. Pour the cranberry mixture into a 13 by 9 by 2-inch glass baking dish. Cool completely. Whisk in the lime juice and vodka. Freeze until the granita becomes slushy, about 2 hours. Using fork, stir to blend. Continue freezing the granita until frozen, stirring every hour to form crystals, at least 5 hours or overnight.
Divide the granita among 6 dessert glasses. Garnish with fresh cranberries, if desired, and serve.
Recipe courtesy of Giada De Laurentiis