Not much more than a major investigation.
Cable disruptions happen. When they do, traffic is rerouted. Usually you have plenty of alternative cables to reroute to along the same path. There are 15 cables between the United States and Europe, although there are other Atlantic cables between other countries and continents. If these were to be cut, we would reroute data through the pacific cables. This would cause increased stress for sure, and might result in some increased ping time to Europe, but communication will continue.
There would certainly be an investigation. Multiple cables being cut at the same time would either be assumed to be a natural event (earthquake) or possibly the Russians. This would raise alarm at the Pentagon, but seeing as how it’s only you cutting the cables, the diplomatic tension would be temporary.
This NPR article mulls over the same question (due to concerns about Russian submarine interference).