Use a sharp chef's knife to cut the watermelon into manageable cubes, removing seeds if present. Measure about 4 cups of the cubed watermelon flesh.
Place the watermelon cubes into a blender. Blend on high speed until the mixture is completely smooth and no chunks remain, approximately 30 seconds. You should see a bright pink liquid with a uniform texture.
Position the fine mesh strainer over a large bowl. Pour the blended watermelon through the strainer, pressing gently with a spoon to extract as much liquid as possible, removing pulp and fibers. The strained juice should be clear and vibrant pink.
Measure the strained juice and, if desired, add a small amount of sugar or honey to sweeten. Stir thoroughly until dissolved, tasting and adjusting sweetness as needed.
Transfer the juice to a pitcher and chill in the refrigerator for at least 30 minutes before serving. Serve cold, optionally garnished with a small watermelon wedge or mint leaves.