Crush the mint leaves lightly with the back of a spoon, to release the oils. Slice your watermelon into cubes and place in a food processor or blender. Purée.
Add the mashed mint into a large pitcher with the 2 cups of puréed watermelon, the rum, simple syrup, and lime juice. Stir to combine.
Pour over glasses filled with ice and garnish with sprigs of fresh mint.