Is there a word for the act of simultaneously pulling and twisting an object?
wrench
Definitions including pulling and twisting follow (M-W).
intransitive verb (2):
to pull or strain at something with violent twisting
transitive verb (4a):
to pull or tighten by violent twisting or with violence
noun (1a):
a violent twisting or a pull with or as if with twisting
Example sentence found online (Pal Item dated June 9, 2019):
Violent winds downed trees and wrenched off tree limbs in a frenzy of nature at its most ruthless.
Synonym: wrest (M-W, English Language Learners Definition, 1 of 2):
to pull (something) away from someone by using violent twisting movements