The term 'cast a slur on' can be summarized as making an ASPERSION, which is a nine-letter word. An ASPERSION is a derogatory remark or statement that is intended to damage someone's reputation. It is usually done in a public setting and is often used to spread false information about someone. Aspersions are considered to be slanderous and can have serious legal consequences if the person making the statement is found to be guilty of libel.