The film's ending is absolute rubbish. It makes no sense and it totally destroys the main character as a human being possessing a human soul. It annihilates all empathy that the story brought to the viewer. I'm not sure what the maker's intention was, either to establish an implausible ending for the story or the movie itself - to enrage people without any particular reason, outside commercial ones. Or to utterly render Joe as a clear homicidal nut-job out of some other reason which I cannot fathom. Of course, I suspect the ending was motivated out of commercial reasons. Make Joe do something totally outrageous and insane, something that NO ONE expects her to do - and then we'll sell big time. Well, congrats... the ending absolutely destroyed all worth Nymphomaniac had managed to instill inside my brain in regard to its message/story.
To me, this stunt pulled at the end is pure bullshit, and it's insulting to me as a viewer - if the film author's intent was to transmit any serious message worth "taking home" with this artistic movie... he failed spectacularly at the end of it.
The end's gratuitous violence and implausible choices DESTROY the whole movie, the whole story, and especially the character.