In a small saucepan, combine the sugar, corn syrup, lemon juice, grenadine, and mint leaves.
Bring to a boil over medium heat, stirring until the sugar is completely dissolved.
Remove the syrup from the heat and let it cool slightly while you prepare the watermelon.
Cut the rind off the watermelon and chop the flesh into large chunks.
Working in two batches, puree the watermelon chunks in a blender until smooth.
Pour the puree through a fine-mesh strainer into a large bowl, pressing on the solids to extract all the juice.
Whisk the slightly cooled syrup mixture into the strained watermelon juice until well combined.
Pour the mixture into a 2-quart freezer-safe container, cover, and freeze for 3 to 4 hours, or until firm. For a smoother texture, stir the mixture vigorously every hour.
Add 1-2 tablespoons (30 ml / 1 fl oz) of vodka to the mixture before freezing. The alcohol helps prevent large ice crystals from forming, resulting in a softer, more scoopable sorbet.
