Remove seeds from watermelon cubes if necessary (though seedless varieties work best).
Place the watermelon chunks, cucumber, mint leaves, lime juice, and sweetener in a blender. Pulse until smooth but not completely liquefied—about 30-45 seconds.
Pour the blended mixture through a fine-mesh strainer into a pitcher, pressing gently with a spoon to extract all the liquid while leaving solids behind.
Refrigerate the strained mixture for at least 30 minutes if time permits.
When ready to serve, fill glasses halfway with ice, pour in the chilled watermelon-cucumber mixture until about ¾ full, and top with sparkling water. Stir gently to combine.
Garnish with fresh mint sprigs, watermelon wedges, or cucumber slices.