As I understand it their immortality works by binding their soul entirely to their body, completely removing its connection to the Aethyr. Thus when they die their soul doesn't move on - because it is too strongly bound to this world and has no path to leave. If you destroy the skull the soul will go to another part of their body because that is the most bound point for it.
Sucking out all the magic away from their soul would keep them from forming a new body as long as it was maintained, but so will scraping off any regrown flesh, or trapping their soul in one of those amethyst jars. It doesn't kill them because death is the soul leaving the mortal realm, and theirs can't.
Notably we have seen one way to kill a vampire permanently: Have it feed solely on Dhar for long enough to become a Vargheist, presumably destroying its soul in the process, and then kill the Vargheist.
Feeding solely on Dhar gets you a Necrarch, I think Varghiests take something more.
I think I've heard Warpstone is involved?
The only known source of Vargheists, or at least the only one I know of, is the Von Carnsteins
They lock their family who have fallen from favor in stone sarcophigi or coffins hung upside down deep inside cave networks under their castles
There the unfortunate vampire is slowly driven mad by their inability to feed, being unable to die of the thirst that wracks their body is apparently the greatest of torments a vampire can ever experience
Over the course of decades water, tainted by both warpstone in the stalagtites they are hung from and the general soil of Sylvania, drips into their prisons, and in their desperation for blood the soon to be Vargheist drinks
Over many years this process causes them to devolve, destroying their mind and mutating their form into a more bestial, batlike creature
Eventually they grow large and strong enough to crack open their prisons, stripped of name and personality, and fly off to tear into the first living creature they can find to finally taste blood again, permanently reduced to a ravening beast
I'll note however that I can't find any indications that a Vargheist isn't still immortal
The process certainly warps their body and destroys their sanity, but I'm unsure about the status of their soul