You could selectively prick the best looking areas along the stem/trunk with a pin or needle...to see if white sap flows. Areas along the stem with white sap are still "alive". Then, that living section can be calloused and planted...and the dead wood discarded. Of course, if you can find live wood going down the trunk directly into the soil, then remove the dead wood above and attempt to revive the rooted living part of the plant.

I would take it out of the sun and give it a BIG drink of water. Let it rest on a shaded area for a while and keep hydrating it, it may plump back up. Keep it shaded until it recovers. I had one do that before and freaked out and cut a branch but then realized it wasn't rot. I rehydrated the plant and it ended up being just fine. It's worth a shot.

However if a cutting is that dehydrated it will most likely not root for you because you can't get it to callous and survive long enough so I wouldn't cut anything more, just get as much water into it as you can.

Good luck and please let us know how it goes!