Sangria is traditionally made with robust red table wine; for this chilled dessert soup, use a light, fruity red, such as a Beaujolais or a Valpolicella.
Place 2 cups of watermelon chunks in a medium bowl. Add wine, cranberry juice, lime juice, sugar, and honey; let stand 15 minutes.
Cut remaining watermelon chunks into 1/2-inch pieces; set aside.
Transfer watermelon-and-wine mixture to a food processor, and pulse until almost smooth, about 30 seconds. Return to bowl; add honeydew, cantaloupe, reserved watermelon, and mint leaves. Stir well, chill, and serve cold.
