slander (verb) to say something about someone that is not true and is likely to damage their reputation
taint (verb) to make someone seem less honest, morally pure etc
smear (verb) to try to damage someone’s reputation by telling lies about them disgrace verb formal to harm the reputation of a person or group by doing something bad or immoral
cast aspersions (on)
to say or write things about someone that attack their character, work etc
