Add your watermelon chunks to a food processor or high speed blender until smooth, about 30 seconds to 1 minute in the food processor or in the blender.
Pour the pureed watermelon into a large pitcher and add in the lime juice, muddled mint leaves and stir. Add in the white rum. Stir vigorously for about 15-30 seconds to incorporate.
Taste and add the appropriate amount of simple syrup based on the sweetness of your watermelon, up to ½ cup simple syrup, and stir again.
Pour into an ice filled glass and enjoy!