Generally, sites that posts mugshots will remove your mugshot if you have gotten your conviction expunged and you present them via email with proof of your expungement. This isn’t due to any law requiring them to, it’s simply a business practice of many of these sites. Therefore, if you get your conviction expunged, you should start contacting the sites again to let them know that this occured.
Expungment means that you’ve filed to have your prior criminal conviction sealed. This makes the records unavailable through the state or Federal repositories.
Getting your record expunged does not guarantee that your mugshot will be removed from a website. BUT, sending these websites proof that your record has been expunged increases the likelihood that a site will remove your mugshot, especially if the site lists expungement as one of its qualifications for removal.