I just found the Clipboard Viewer app while searching for a similar sort of problem. That might help you identify something in the clipboard that you can then query in an If Then Else action using The Clipboard: System Clipboard conforms to and entering the public or private UTI (see Apple Uniform Type Identifiers) type name for one of the ones listed in General Clipboard for the copied effects data to at least filter out anything except the type of clipboard data you want to process.
As to how to save and paste later, this post might have some helpful info on using the Clipboard History Switcher or named clipboards to save the data.
But as for saving to/restoring from a file, especially when dealing with data from a third party app, that would be a lot trickier and more error prone.