How exactly you define anime in cases like that can be an interesting question. The word anime is used in Japanese to describe all animation, I believe, and I have always taken it personally to refer simply to all animation produced in Japan. There is no doubt that anime has also come to refer mainly to a specific style or group of styles however.
Incidentally, and slightly related, some dude at a convention once told me that the proper proununciation of anime is 'an-ee-me' rather than 'an-ee-may'. Anyone know if this is correct. I have advanced pedantic wanker syndrome and like to pronounce foreign loan words correctly, sometimes even putting on a slight accent to really get a lovely schadenfreude or smorgasbord or whatnot. Of course I guess I could just pronounce anime as in the French 'dessin anime', which I believe is where the Japanese take the term from anyway.
Anyway, that Franken Fran manga I was talking about earlier. It's really fantastic. I would describe it, improbably, as a light guro comedy, somewhere between the more comedic parts of the work of Shintaro Kago and Masamune Shirow. There's lots of body horror and some nudity but it generally avoids the really explicit sexual violence stuff you often find in the guro genre. Still totally NSFW and probably NS for normal people as well. Basic description: Our main character, Fran Madaraki is a polite, charming, slightly ditzy revenant, apparently stitched together from corpses by a mysterious scientist who is heavily implied to have been a major force behind Unit 731, as well as possibly being immortal. She is a supernaturally gifted surgeon: She will
never allow a patient to die if she can help it, and she will
always do what the customer wants. She also believes powerfully and naievely in true love. From these three things emerge some pretty nasty horror and pitch black comedy. Generally, Fran unknowingly acts as an agent of karmic justice. For example, in the first volume, a rich businessman leaves 90% of his estate to his playboy grandchild. The father, who has been skipped over in the inheritance, has his own son murdered, then asks Fran to bring him back to live, thinking she will create an emotionless, pliant zombie. Stirred by the powerful love of a father who will do anything to bring his dead son back to life, Fran puts the businessman under anesthetic, carves out half his brain, installs his sons brain in his skull and attaches his dead sons face (the son remembers exactly who had him killed) to the back of his own head, with a modification made to his neck so that it can swivel around 270 degrees, allowing the two faces to take alternating control of the body. Hilarity ensues!
You can read it all
here