Use a mortar and pestle to mash the mint leaves. Remove and discard the rind and seeds of the watermelon. Put the fruit into a food processor fitted with the steel blade and puree. Put the mashed mint into a large pitcher with 2 cups of pureed watermelon, the rum, simple syrup, and lime juice and stir to combine. Pour the mixture into a pitcher for serving.
Place ice cubes in 6 glasses and pour the mojito mixture into the glasses. Garnish with sprigs of fresh mint and spears of watermelon. Serve ice cold.
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