Cut watermelon in chunks in batches. Place in blender; cover. Blend for a few seconds. Pour through a strainer into a large liquid measuring cup. Discard pulp. Continue cutting and blending watermelon until there is 3 cups of juice.
Place juice in pitcher. Add 2 tablespoons sugar and Nestea; stir until dissolved. Stir in vodka and lime juice. Cover; refrigerate until ready to serve.
Rub glass rims with a cut lime; dip rims into granulated sugar to coat rims. Fill glasses with ice; garnish rims with lime slices. Add punch to glasses, not filling all the way to the top. Top each with 2 to 3 tablespoons mineral water.