If you make a false accusation against someone or spread lies about how awful they are, you're calumniating.
The courts would call the act of calumniating "slander." Everyone else would just call it mean. Calumniate is just a fancier way of saying "to lie" — but specifically lying to tarnish someone else's reputation. If your sister said you purposely broke a vase and you didn't, she calumniated. You could calumniate to the principal about your teacher being a lazy, wretched mess — but the other students would probably speak up and prove you wrong.
