Combine 3 cups water and sugar in a medium saucepan; bring to a boil, stirring until sugar dissolves. Stir in chopped mint. Remove from heat; cool completely.
Strain sugar mixture through a sieve into a 13 x 9-inch baking dish; discard solids. Stir in bourbon. Cover and freeze 8 hours or until firm. Remove mixture from freezer; let stand 15 minutes. Scrape entire mixture with a fork until fluffy. Place about 1/2 cup granita in each of 8 small bowls or glasses; serve with 1 lime wedge. Garnish with mint sprigs, if desired.