Blend: Working in two quick batches if your blender is small, combine the watermelon cubes, cold water, fresh lime juice, and sweetener (if using) in a blender. Blend on high until completely smooth and liquefied.
Strain (Crucial Step): Set a fine-mesh strainer over a large pitcher. Pour the blended mixture through the strainer. Use a spoon to gently stir the liquid in the strainer to speed things up. Discard the thick, frothy pulp left behind. This leaves you with a beautifully clear, crisp juice.
Chill: Place the pitcher in the refrigerator for at least 1 hour to get it ice-cold.
Serve: Give the pitcher a quick stir just before serving, as natural separation will occur. Pour over glasses filled with ice, and drop a lime wheel and a sprig of mint into each glass.
Make-Ahead & Storage Tips