Cut the watermelon into chunks and remove the rind. In a blender, combine the watermelon, lime juice, and mint leaves, if using. Blend until completely smooth. (The key to this juice having a good flavor is the watermelon; make sure it's ripe and sweet before you begin.)
You can serve this juice right away if you don't mind the watermelon pulp. Or, you can pour it through a fine-mesh strainer if you prefer a totally smooth drink.
Serve watermelon juice over ice, and garnish the glass with sliced lime. Leftover juice can be stored in an airtight container in the fridge for up to 3 days.
Notes
Nutrition information is for roughly 1 cup of watermelon juice. Typically you'll get at least 5 cups of juice from a 6-pound watermelon.