In batches (unless your blender is huge), add the chopped watermelon. Add a splash of water (about 2 tablespoons) and pulse until completely pureed, about 1 minute. (If you're adding a bit of sugar, you'll want to add the sugar amount you desire and just as much water to a small saucepan; heat until the sugar dissolves and then add the sugar/water mixture to the blender.)
Line a sieve with a few layers of cheese cloth. Place the sieve atop a bowl or large pitcher. Pour the watermelon puree into the cheese cloth and allow to strain--it may take around 5 minutes or so.
Repeat the blending and straining process with the remaining chopped watermelon. Transfer the watermelon juice to the refrigerator for 1 hour to chill. Divide the watermelon juice amongst glasses.
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