Combine 2/3 cup water and 2/3 cup sugar in small saucepan. Bring to boil, stirring until sugar dissolves. Boil 1 minute. Cool syrup. Stir in lemon juice.
Puree green grapes and half of lemon syrup in blender (some bits of grape peel will remain).
Transfer to 13x9x2-inch metal pan. Puree red grapes and remaining lemon syrup in blender.
Transfer to another 13x9x2-inch metal pan. Freeze 1 hour. Stir with fork every hour until frozen, about 4 hours.
Meanwhile, dip grape clusters into 2 tablespoons Muscat wine to moisten, then dip grapes into sugar to coat.
Place grapes on small tray and freeze until frozen, about 4 hours. (Granitas and grapes can be made 1 day ahead. Cover separately and keep frozen.)
Using fork, scrape granitas down length of pan, forming icy flakes.
Pour 2 tablespoons Muscat wine into each of 6 wide glasses. Divide green grape granita equally among glasses. Spoon red grape granita alongside green grape granita in each glass.
Garnish each with sugared grape cluster and serve.
