What makes you think there is not already in place a way to shut it down ?
Certainly easy to close at the shoreline where it comes ashore.
Satellites receivers can be turned off.
The addressing system of tcpip will try and find a way around the
breaks but it should be possible.
The real question would be is it better to leave it on or off.
If the country is isolated but the internet working internally it is
quite easy to make international connections by a way I won't mention.

Belly, when those Islamic alleged terrorists were arrested last week
there was a news video of the house, did you notice the pole and the
wire leaving it ?
I wonder what they found inside ?