I want to know whether native English people have and use a verb form for the noun "taxidermy"?
It would really help if you can tell me a word that is really used or you have heard. And coining new terms is not what I am looking for, I really appreciate any answer though.
There's no related verb form for that as far as I am aware either. We would indeed most commonly use "to stuff", depending on context.
A taxidermist (noun) is a person who carries out taxidermy, and either taxidermic or taxidermal would be acceptable as the adjectival forms.