No advice at all about a stone dam. I personally have never heard of such a thing.

However, I would get the water pressure off of the dam ASAP to mitigate the damage.

Probably the easiest way would be to get some siphons running. There are videos on the internet for starting siphons with inexpensive corrugated plastic drain pipe.

If you can drain the pond low enough to get the pressure off of the dam, but still have enough water in the bottom to save fish?, then you can examine the dam and get the right kind of contractor to perform the repairs, hopefully.