So ignoring the technical problem of how it could actually be done, let's assume we somehow did it, cut every cable, and somehow blocked every cell tower and satellite from somehow connecting to North Korea to the rest of the world.
For the average north korean citizen, probably nothing much changes, most of them don't have much access to the internet to begin with.
For those who do, the elites, people in university, those government, military, etc. it will probably worry a bit.
For the elites who get to enjoy the internet as a luxury, probably not too much changes. I doubt that except for maybe the very top echelons of DPRK society, the Kim family for example (and maybe not even some of them,) anyone is getting totally unrestricted access to the global Internet. They're probably limited to mostly a bunch of north korean-hosted websites, and unless they're relying on data centers and such abroad (and they very well might be,) there's not really much we can do to take them down unless we really want to go in and attack all of the internal Internet infrastructure.
It's going to hamper their universities and such, sucks for them, probably no great loss for the world, the next big scientific break through probably wasn't coming from the hermit kingdom anyway.
It will definitely hurt their ability to conduct espionage, cyber attacks and such, that goes both ways though and it also makes it harder for other countries to spy on them.
They will do their usual sabre-rattling in response, maybe even going a bit above and beyond their usual mostly empty gestures, but probably nothing that's going to lead to any actual escalation p