Combine 2 cups water and the sugar in a microwave-safe bowl; heat in microwave on High for 5 minutes. Stir the mint into the water; let stand for 5 minutes. Strain and discard the mint leaves from the syrup; set aside.
Stir the lime sherbet, lime juice, and 1 cup water together in a large pitcher until well combined. Pour the mint-infused syrup into the mixture. Add club soda and stir. Serve over ice. Garnish with lime slices.
