Submarine cables have actually been tapped in the past, so cutting them should not be much of a challenge. Blind Man's Bluff [1] is a book about this kind of thing (and all sorts of weird things that involve intelligence operations performed with submarines). It is one of those books that would not work if it were fiction: too unrealistic.
[1] https://www.goodreads.com/book/show/42343.Blind_Man_s_Bluff