I'm NOT a lawyer but doing a little (very little) research seems to lead that you would have to sue the poster, and can't sue the website owner. If you win against the poster, thedirty will remove any comments that the courts deemed to be false, but they will probably not remove the whole post, just the lies. In the past a company I was with would remove things for people a lot easier, but thedirty is not a very nice website and my company did not allow that sort of thing anyway. Thedirty is more of a revenge type site, IMO.
Section 230(c)(1) of the 1996 Communications Decency Act provides immunity from liability for providers and users of an "interactive computer service" who publish information provided by others:
No provider or user of an interactive computer service shall be treated as the publisher or speaker of any information provided by another information content provider.
https://www.law.cornell.edu/uscode/text/47/230
By user in that law, they aren't talking about the poster, just any other user on the site.