If a website is using a picture of me with my approval, can I have them take it down

The photograph has nothing to do with you, unless you are saying that it is part of the disparaging posting in the sense that someone is falsely and claiming that it is you. Even then, if it is obviously not you (say it is a picture of a monkey or a famous person) the photograph could not be defamatory, but merely a (mean) expression of opinion. It is as if the person who posted is saying that you are "just like" the picture. That is a terrible thing to do, but in the United States it is perfectly legal.

Disparaging comments or depictions of a private person in a false light are only legal defamation if they are false statements of what seem to be facts, and the person writing those statements knows or should know they are false -- and you are able to prove that you have really been harmed, and not merely had your feelings hurt a little. It usually makes it worse to bring a lawsuit to "solve" Internet-based defamation, because most claims are not resolved favorably for the plaintiff, while the posting itself gets a lot more attention than it otherwise would.