Combine water and sugar in a 2-cup glass measuring cup; stir until sugar dissolves. Add ice to reach ½ cup; stir until ice dissolves. Add coconut rum, pineapple juice, lime juice and mint. Pour into a pie plate and freeze for 1 hr. Use a fork to scrape up forming ice crystals; return to freezer for 1 hr. Scrape surface of the granita again with a fork; return to freezer for 1 hr. more or until solid. Scrape again and scoop into 2 lowball glasses. Garnish with mint and serve immediately.