In English I know of two colourful terms for blowing your nose without use of a handkerchief or tissue by holding one nostril closed and expelling mucus from the other:
In English we would never use the plain turn of phrase to blow one's nose for this act, even if we didn't know the slang/jocular terms I listed above we would use some circumlocution to describe the (to us) irregular method of nose blowing.
Yesterday morning I saw a nice young lady perform this manoeuvre in the street outside my hotel in a town outside Chengdu, Sichuan. This cemented the notion I already had that this act is not stigmatized in Chinese culture. But I'm not sure whether it's considered a normal or plain way to blow one's nose using the usual Chinese expression for nose blowing.
Is there a slang, jocular, or colloquial term (or any other kind of term) for this act in Chinese? (I'm most interested in Mandarin but other varieties of Chinese are also interesting.)