To means to spread malicious, false statements about someone to damage their reputation. It is essentially a formal way to say you are lying about someone to make them look bad. Essential Guide to "Calumniate"
: To make false and defamatory statements maliciously.
: A classic example is a politician spreading a false rumor about a rival to win an election. What is the meaning of the word calumniate? - Facebook
: Unlike simple "lying," calumniating specifically targets a person's character or reputation with the intent to harm.