Place watermelon in a food processor and process until smooth. Pour the pureed watermelon into 2 empty ice cube trays and freeze until firm, at least 4 hours. Place 8 martini glasses in the freezer to chill.
Place 2 cups of the watermelon ice cubes and the remaining ingredients in a blender and blend until smooth. Pour into 4 glasses and repeat with the remaining ingredients. Garnish each glass with a watermelon wedge.