Signed PDF: how to "save a copy"?

I'm sorry, but the message is lying. Internally to Acrobat, the only difference between SaveAs and Save a Copy is which PDF is open after the save. SaveAs reopens the file you just saved. Save a Copy saves the file but leaves the original document open. There is no way you can edit a signed file. To remove your signature, right-click on the signature and take the drop-down option to delete it.

I've not seen this message except when someone clicks "view signed version" in a signature panel item. That opens an earlier version of the document (i.e. just after that signature was applied) for viewing in read-only mode. Since it's not a file in itself (it's a prefix of the open file), it needs to be saved as a stand-alone file before you can do anything with it. In this case, only SaveAs makes sense.