Make the mint syrup: Add water, sugar/xylitol, and mint twigs into a small pot, bring to a boil. Rub the mint with a spoon into the sides of the pan, helping it release as much flavor as possible. Leave to cool completely then discard the mint leaves.
Using a tablespoon or an ice cream scoop, scoop out the watermelon pulp. Transfer to a food processor and blend thoroughly, then strain through a sieve. Seeds and dry watermelon pulp should stay on the sieve. From 4.4 lbs (2 kg) 'mini' watermelon, I had 3 lbs (1.4 kg) watermelon flesh and then after blending and straining it about 4 cups (1 liter) watermelon juice.
In a big pitcher, combine the watermelon juice, lemon juice, water, and mint syrup.
Serve chilled, optionally with ice cubes.
Enjoy!