Add the chilled watermelon to a blender and blend until completely smooth. You should have about 4 cups of watermelon puree.
Pour the puree through a fine-mesh strainer into a bowl to remove any pulp.
In a large pitcher, whisk together the cold water, fresh lemon juice, and granulated sugar until the sugar has completely dissolved.
Stir the strained watermelon puree into the lemonade mixture until well combined.
Add ice and fresh mint to the pitcher, or place them directly into individual serving glasses before pouring in the lemonade.
Serve immediately or refrigerate until well chilled.