Not Sure How -- S P O I L E R

He dies; he would have come back to kill her if he hadn't. I think there is a somewhat supernatural angle.The Reverend says near the end that as a doomed man he can do anything. The movie seems to imply that his lust for his daughter put him outside moral rules, and thus gave him increased strength. Instead of moral fortitude, he had immoral physical strength. Is that supernatural though or is that a placebo effect? It seemed kinda silly to me how the Reverend was able to kill so many people without resistance; especially, the gunslinger. I would think the gunslinger would have more strength and experience to at least put up a fight.

I would say the biggest flaw in the movie is this quasi-supernatural angle. It seems rather incompletely conceptualized and the movie uses it inconsistently.

Like her friend/lover, the real Liz, I think she only just sliced the skin and underlying tissue, so it would have bled a bit and left a scar, but nothing more. Of course, she wanted to kill him but freak ‘accidents’ happen where people survive even the most serious injuries, which potentially this wasn’t actually. I didn’t recall anything unusual with his voice later, so she couldn’t have gone deep as his voice box wasn’t damaged and also the cut was only a slice to the front of the neck and must not have touched the arteries which are more to the sides of the neck.
My partner felt there was a supernatural element to the father/preacher too; I did not. I felt it was cinematography and directorial choices, especially for the highly ridiculous scene where she sets him on fire and he continues to stand there and talk to her.

Yes he died. It is difficult to do this in a film and not have some loose ends, but there is a great deal of hints and references in the movie that address this and parallel themes.

As the newly arrived preacher, he indicates that hell is worse than people realize, as if he's been there. Also, when she sets him on fire, he is mostly unaffected, citing that the pain in hell is not from fire, but from absence of love. He falls out the window, but we do not see him again. He has perhaps returned to hell.

Also, earlier when he is dragging Joanna through the mud, she says " I will kill you" to which he replies "that will not stop me" .

The director was influenced by Sergio Leone and his spaghetti westerns. Another person who was influenced by Leone was Clint Eastwood who made High Plains Drifter about a man who was a ghost that returned to carry out retribution, which is a prominent theme of this movie. Also, hell featured prominently in HPD as well and included several shots of fires burning, and the town renamed Hell.

In Pale Rider, by comparison, the preacher is also a ghost. In contrast, the preacher is not succumbing to the forces of evil. In Brimstone, the preacher is unable to overcome his lust for the young girl who despises him and becomes obsessed with her.

In Pale Rider, the preacher resists the outward advances of the young girl. The preacher ends up finding retribution by killing the Marshal and his deputies, although he had not necessarily been seeking out retribution. Pale Rider was not likely a real preacher, but acted righteously and ended up protecting his flock against danger.

In Brimstone, the preacher was merely self righteous, and succumbed to the devil. He warned of false prophets and wolves in sheep's clothing, but he turned out to be that very wolf .

I got a little off track, but yes, he was a ghost in parts 1 and 4 when his eyes were black, and human in parts 2 and 3 when his eyes were blue.