Combine peach nectar and sparkling water in a 9-inch square baking pan. Freeze mixture 1 hour, scraping with a fork every 15 minutes to make a slushy mixture.
Wet top of each glass, and swirl in sugar. Add 1 teaspoon grenadine to each glass, and top with 3/4 cup peach nectar mixture. Garnish each with a skewer of peach, lime, and mint. Serve immediately.