There's not much need to go into detail on the plot. Simply put, The New York Ripper is the story of a mad killer with a penchant for slashing young woman and harassing the police with his duck-like voice. That's really all you need to know.
The New York Ripper is Lucio Fulci's latter day ultra-violent take on the Giallo. When I say ultra-violent, I mean ULTRA-violent. If you're a fan of Fulci-style gore, there's surely something here for you. There's one scene where a girl's eye meets a razor that's particularly nasty and particularly difficult to watch. And, if you're a fan of Fulci-style sleaze, there's surely something here for you also. While I won't go as far as some reviewers and call it pornographic, there are a variety of sexual perversions on display. But it's not all blood and sex. Fulci actually manages to create a few scenes with real tension. There are moments where you know that killer is about to strike, but the anticipation Fulci builds in the audience is quite good.
Unfortunately, there are problems I have with the film. I'll limit this to two examples. First, the resolution of the mystery is a real letdown. The killer's identity is far too easy to guess. Fulci telegraphs the answer form the opening moments of the film. Second, Gialli often ask the viewer to suspend reality to accept various plot points, but the final scenes in The New York Ripper cross the line into ridiculousness and really hurt the overall film. I'm certainly no expert, but I sincerely doubt that all the psychological babble made any real sense to anyone.