I'm not aware of any attempt by the Nazis to destroy the transatlantic telegraph cables and I'd be surprised if there was, it would be a lot of effort for very little return.

Firstly, U-boats are not well suited to finding and destroying undersea cables. The method used at the time was to drag a specially made grapple along the sea bed until it caught on the cable. A U-boat would have had to been modified, no doubt with a large number of technical difficulties to mount and use such a device. In addition it was not guaranteed to be a quick progress, taking hours or even days to correctly find and snag the cable.

Attempting to use a traditional ship to cut the cables would run into the general problem of Allied sea superiority. It would be next to impossible for a German cable breaker ship to sneak out of harbor, make it to one of the cable locations and spend time trawling for it without being noticed or destroyed.

Further, severing a single line would have had little effect on communications, there were numerous cables crossing the Atlantic, here's a map of the undersea cables in place fifty years earlier https://collections.leventhalmap.org/search/commonwealth:7h149w146 By the time of WWII the number had only grown. In addition, much of the Allied communication took place via encoded radio signals.

As one further nail in the coffin of the plan, the cables would not have been overly difficult to repair, the locations of breaks in the cables could be determined by measuring the electric resistance of the cable, then it was only a matter of going to the approximate location, trawling to find both ends of the cable and splicing them together.

Related: how feasible would it have been to destroy transatlantic cables?