Moderating online education forums: delete, snip or leave rudeness?
Snip the last part out, send a private message to the poster reminding them of the behavioral standards expected in the course forum.

I don't see any reason to remove the whole post, if there are parts that are appropriate. Removing the whole post makes it seem like your motivation is to punish the poster, rather than to keep the forum professional and constructive.

I would recommend against leaving rude comments there until/unless someone takes offense. This is a forum that is hosted and moderated by you, not your students. It is your responsibility as an educator to create a constructive learning environment (to the extent that you can). It's not your students' responsibility - they have to be responsible for their own actions, but they shouldn't have to be responsible for making you respond to other students' actions.