The US says that Russian submarines are patrolling intensely around undersea communication cables.

This may be true, but I doubt that Russia is interested in cutting these cables. What would be the point of doing so? That would alienate the whole world, not just the US.

Standard intelligence strategy is, "Don't block the enemy's communication, listen to them." We already know that the NSA taps cables; I suppose Russia is looking for ways to do likewise.