I think you could probably remove classification tags and markings by selectively copying content from a classified email and pasting it into an new, unclassified email.
Not on the same computer, though. The person would have to bridge the air gap between classified and unclassified systems. That is not easy, and it had to be done intentionally, with use of unorthodox methods. You can copy and paste whatever you want on a secure computer, but the bits will stay there. FSOs and their IT staff spend a lot of time on making sure that unauthorized copying of data is as difficult as possible.