In response to your 'biological knowledge' - In any instance, if a human was to have their neck twisted the same way Rem had hers, they would 100% die, so you're correct in your thoughts there.
The best way to consider this is to think of it as 'Anime/Manga/Novel Logic' and accept it, though I know that's not an acceptable answer, so I'll attempt to give reason to her survival.
The idea that she was torn in half should be forgotten when talking about the anime, as that wasn't the case, though as for how she survived in the novel is beyond me and I don't want to attempt to guess at how she survived.
As for how she survived in the anime, that would come down to a few things.
- Life force. If she were to have a large amount of life force, which I assume she does, as she is a demon (it's known in multiple novels and such that demons have a much larger life force than that of humans), it's safe to assume she also has this trait.
- Willpower. This one is a bit iffy and is more of a placeholder to further the point, though may not have any relevance. If someone has the will to carry on living, especially with the amount of willpower she shows (she states that the cultists took her "reason to die" when they took Subaru, meaning she was willing to die for him), it's not too far a stretch to say she would use any and all abilities to stay alive in order to free him, which she does. It's plausible that she was using magic to keep herself alive, though that's speculation, without proof.
- Biology. We can't say for sure that she has the same anatomy as humans and that she would react the same to the treatment as we would, so we can't rule her dead after the treatment, even if we do see it as logical. We could say that the body contortions that were applied were simply hindering her ability to move and her death came from the damage she sustained on her journey to where Subaru was being held. (We know she had lost a lot of blood, as we witnessed her get a knife lodged in her left shoulder earlier, as well as her arm burned.) Thinking that she would make it to Betelguese and his hideout without receiving further injury is an insult to writing, so we'll assume she took damage (as well as the blood dripping down her head, as well as tattered clothes, it's safe to assume her journey was rough). All that damage could have been the underlying factor in her death.
We can't really say for sure why she survived as we don't know 100% how her anatomy works, how much of a play on her life the willpower and life force come into it, as well as a few unconsidered factors that I forgot to mention.