The internet was originally DARPANET. From the Defense Advanced Research Projects Administration. It was constructed on OUR infrastructure. And we can only shut down OUR portion. We can't possibly shut down ALL of it. There is no way to do so without violating other countries sovereign territory. BUT it's well within our rights to shut down the US communications systems altogether.
"I would rather be exposed to the inconveniences attending too much liberty than to those attending too small a degree of it." Thomas Jefferson