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Muddle the mint.
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Remove and discard the rind and seeds of the watermelon.
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Put the watermelon into a food processor fitted with the steel blade and puree.
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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.
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When ready to serve pour the mojito mixture into the glasses on ice, and garnish with sprigs of fresh mint and slices of cucumber. Serve chilled.