Pour the rose into ice cube trays and freeze until solid, at least 6 hours or preferable overnight.
Place the watermelon on a baking sheet lined with parchment paper and arrange them so that the cubes are not touching each other. Freeze from at least 2 hours, then transfer to a container or zip-top bag and keep frozen.
Make simple syrup if necessary. (See recipe in Condiments section)
Place the rose ice cubes, frozen watermelon, mint simple syrup, and lemon juice in a blender and blend until combined and creamy. Pour into glasses and garnish with a sprig of mint.