If something is scurrilous, it's meant to offend. Scurrilous rumors can give you a bad reputation, and scurrilous stories sell tabloid magazines.
If you say something scurrilous about someone, your intentions are bad: you mean to damage their reputation or insult them (or quite possibly both). Writing an article for the school newspaper in which you claim that your math teacher has a secret life as a circus clown could be seen as a scurrilous attack, unless she proudly moonlights entertaining kids with her juggling skills. This adjective comes from the Latin scurrilis, "buffoonlike."