Puree the watermelon: I throw the diced watermelon in a blender and blend until smooth.
Strain: I pour the juice through a fine mesh strainer into a large pitcher, pressing with a spoon to get as much liquid as I can.
Muddle the mint: In the pitcher or a separate bowl, I gently muddle the mint leaves with a muddler or spoon.
Mix: I add the rum or vodka, fresh lime juice, and simple syrup to the strained watermelon juice. I stir it well to combine.
Add soda: I pour in the chilled soda or sparkling water and stir gently.
Serve: I fill each glass with ice, pour the mixture over, and garnish with mint and watermelon.
For a smoother drink, I sometimes strain it once more before pouring. If I'm making this for a group, I just double everything and serve from a pitcher.