How can we remove On-line Arrest records (mugshots)?

Are you talking about the bottom-dwellers who own mugshots.com? They're offshore and beyond the reach of American law. I am unaware of any litigation that has been successful here. They're despicable. Of course, the problem started with this "transparency" trend by arresting agencies to post booking information and mugshots on-line. You have to wonder what their real agenda is.

Privacy died with the advent of the internet. These sites will charge you to remove the mug shot. Otherwise, you could pursue litigation, but it's not slander nor libel if it's true. They obtain publicly available records and publish them. Unfortunately, it's not illegal, but it is distasteful.

Unfortunately, these sleazebags are hard to fight. There have been several lawsuits against them, but nothing that has shut them down yet.

You can't - you can pay them money to take it down, but there's no guarantee they will or that another similar site will not soon appear.

These websites are very loosely run. You can pay to have it removed, but it's hard to guarantee anything.

Newly amended Civil Code 1798.91.1 now says that a webmaster cannot solicit for or charge a fee to remove a mugshot. Unfortunately they don't have to remove them, but it takes the profit edge out... allegedly. Perhaps a stern letter from your attorney may prompt them to remove it. Best of luck.