Unlikely to happen, for several reasons:

1) Putin or any government cutting the Transatlantic cables could be seen as an act of war.

2) The Internet would just route around the issue(s).

3) Any ship caught cutting cables in the Atlantic would greeted by the US/UK Navy.

4) As someone else pointed out, there are a lot of Transatlantic cables, so it actually might be hard to cut enough of them to make an impact.