This is one of those big "what if bad stuff happens" questions.
"Fewer than 300 cable systems transport almost all transoceanic traffic around the world. And these often run through narrow pressure points where small disruptions can have massive impacts. Since each cable can carry an extraordinary amount of information, it’s not uncommon for an entire country to rely on only a handful of systems. In many places, it would take only a few cable cuts to take out large swathes of the internet. If the right cables were disrupted at the right time, it could disrupt global internet traffic for weeks or even months."
From:
Cables
Comments
https://en.wikipedia.org/wiki/Operation_Ivy_Bells