Cherry picking is a fallacy where only select evidence is presented in order to persuade the audience to accept a position, and evidence that would go against the position is withheld. The stronger the the withheld evidence, the more fallacious the argument.
Quote mining is a form of cherry picking, and the genuine points used in construction of straw man arguments are typically cherry-picked.
Dr. Jones and Dr. Smith published an article in the Klingon Journal of Vaccine Evil which proves that vaccinations cause a third eye to grow out of the child’s head. Based on that evidence, vaccines should be outlawed.