In a small saucepan over medium-high heat, heat sugar with 2 tablespoons water, stirring occasionally, until dissolved, 1 to 2 minutes; set aside.
Peel, seed, and coarsely chop melon. In a food processor, puree melon with sugar syrup until smooth (to yield about 6 cups); pour into a large, shallow dish.
Freeze, stirring and breaking up crystals with a fork every 30 minutes, until entire mixture is frozen and crystallized, about 3 hours.
Breaking up the frozen mixture periodically with a fork creates the sparkling crystals that are characteristic of granitas.