Over 99% of the transcontinental internet traffic goes through a network of 280 sets of undersea cables.

How vulnerable are these to deliberate sabotage by the major powers? 

I'd rather not focus much on why any nation would want to attempt such a thing or to what degree principles of MAD will apply, I'm just assuming that it's a war scenario and such intentional sabotage is desirable.

Such sabotage won't actually shut down the internet rather it would only slow it down. If the slow down is significant enough it could have serious impact on productivity, and it would cost more to send the same amount of data. Or certain kinds of internet traffic might get banned altogether by the governments in favour of maintaining higher bandwidth for more important traffic. Again this is another discussion that's out of the scope of this question, also it's not something that's easy to predict and will depend on the nature of the war/emergency. 

I'm just asking how much would it cost to do it (sever say, 50% of the cables)? Is it possible at all? What technology would work best (I'm assuming some sort of robots but not 100% sure)? 

Also take into account the fact that the sabotage operations will probably have to be geographically distributed and/or fast and/or discreet enough (with options for plausible deniability and blaming others nations for the sabotage) ... If you set up an entire city just to create the infrastructure required for the operation there's a good chance you could get bombed or nuked before the operation succeeds.