In a 9” x 13” baking dish (or whatever baking dish you happen to own), combine vodka, grape juice, ginger ale, lime juice and chopped mint. Cover tightly with plastic wrap and place it in the freezer.
Use a fork to stir the mixture ever 45 minutes, making sure to scrape the edges and break up the ice as the mixture freezes, until your granita is completely frozen and has the texture of a snow cone, about 3-4 hours.
Scoop the granita into small bowls or cocktail glasses and garnish each with a few grapes and sprig of mint (if using). Serve immediately.