Remember the Argentinians sunk a five billion dollar British destroyer with a $250,000 dollar Exocet missile.
To my way of thinking the only real threat to a large deck CVA (actually sinking it) would be from a large, heavy-weight torpedo designed to snap a keel. A mine could do the same thing, but a carrier isn’t likely to be steaming over a minefield — except perhaps in the Gulf. Hammering away at aircraft carriers with bombs, kamikazes and so forth may kill a lot of crewmen and take the carrier out of battle. But the vessel itself is a very compartmentalized and the crews are (supposed to be) well versed in damage control.
USS Franklin, USS Forestall, USS Enterprise, USS Oriskany... all these ships suffered devastating attacks and fires and all survived.
Several US carriers lost in WW2 were actually sunk by our own cruisers & destroyers because they were dead in the water. But they were still afloat. Given the lengths the US went to to repair that destroyer hit in Aden, I’d say we aren’t going to finish off one of our own carriers. Very bad for morale.