Peel, clean and scoop each melon into 1-inch balls and place into a zip-top bag or other sealed container. Freeze overnight.
In a small saucepan, heat lemon juice, lime juice and sugar together over medium heat. Stir to dissolve sugar. Remove from heat; let syrup cool.
In a large pitcher, combine lemon-lime syrup, grape juice and sparkling water ; stir to blend. Add frozen fruit to your serving container. Pour juice mix over fruit. Garnish with mint, if desired.
Store any remaining punch in refrigerator for up to 2 days.
For an easy cocktail version of the punch, add 1 ½ cups of light rum to the juice mix.