Put the watermelon cubes in a blender and pulse briefly to puree, leaving some texture to them. Transfer the watermelon to a container with a pour spout. Taste, and sweeten with a little sugar if it's too tart.
To serve, pour the watermelon soup into clear bowls, glasses, or mugs. Garnish each serving with a bit of cucumber, bell pepper, apple, pomegranate seeds, and mozzarella. Alternatively, set the bowls of soup on a buffet, next to small serving bowls containing the vegetables, fruit, and cheese, and let people garnish their own soup.