It's probably much easier to quietly splice a cable when someone else is caught severing it elsewhere.

This is more the NSA's territory and they avoid splicing if at all possible and instead shave the cable.

Necessary link: Operation Ivy Bells http://www.specialoperations.com/Operations/ivybells.html

Also, everyone read the book "Blind Man's Bluff"

You don't have to go back that far https://www.google.com/search?q=undersea+fiber+optics+tapped

The first thought that popped into my head was Dirk Pitt.

I suspect the infamous Mossad Shark http://en.wikipedia.org/wiki/Israel-related_animal_conspirac...

What would be the motive?

Eavesdropping.

http://en.wikipedia.org/wiki/Operation_Ivy_Bells is An example. It is rumored they can do that on fiber, too (http://cryptome.org/nsa-fibertap.htm)

But that doesn't explain why they were cutting it.

I think the many-parent's idea is: cut it in one place in an obvious way, then while the cable is known to be cut, insert your splice in another place. That way no-one notices the few hours' disconnection while you put the splice in.