I do that a little bit, but only with the dry, calloused hangnail bits, and usually only to keep them from snagging on hair, clothing and upholstery (because when it snags it hurts).
I'm more likely to use a nail-clipper if I can find one, but I'll use my teeth or the nails of the other hand if none is available. I never deliberately go deep enough to get to nerves and blood, though.
I definitely chew my kips; it's a habit I can't seem to quit and with that I do sometimes get down to the capillaries and bleed. I also pick scabs; I used to do the pimples on my face, until I got tired of looking at moon hash in the mirror; now I only pick scabs from parts of my skin that don't show when I'm dressed.
Also I have a lot fewer pimples on my face than I did when I was teens and early twenties.
My husband chews his nails and cuticles down to the quick. I think he's neurotypical because he relates well to people and calls social skills a "no-brainer" rather than something he has to analyze and can explain. By this I infer that he does it intuitively. But he does have a few autistic traits, including things that almost seem like stimming. Predominantly the "wolf-biting" and knuckle-rubbing that he does.
Yeah--I do think that wolf-biting must be a type of stimming.
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Your neurodiverse (Aspie) score: 141 of 200
Your neurotypical (non-autistic) score: 71 of 200
You are very likely neurodiverse (Aspie)
Official diagnosis: Austism Spectrum Disorder Level One, without learning disability, without speech/language delay; Requiring Support