Place the chilled watermelon cubes into a high-speed blender. Pulse and blend on high until the fruit is completely liquefied and smooth.
Position a fine-mesh strainer over a large pitcher. Pour the watermelon puree through the strainer to remove any remaining pulp or fibers. Use a spoon to press the solids to extract as much juice as possible.
In a separate small bowl or measuring cup, whisk together the fresh lemon juice and the sugar until the sugar has completely dissolved. This ensures your lemonade isn’t grainy.
Pour the lemon-sugar mixture into the pitcher with the watermelon juice. Add the 2 cups of cold water and stir well to combine all the flavors.
Taste the lemonade and add more sugar or water if needed. Fill glasses with ice, pour the watermelon lemonade over the top, and garnish with fresh mint and lemon slices.