My goal: make Excel save a copy of the workbook in a folder different from the original folder where the workbook is and as well with a timestamp.

This code runs correctly:

Private Sub Workbook_BeforeClose(Cancel As Boolean)
  ThisWorkbook.SaveCopyAs Replace(ThisWorkbook.FullName, ".xlsm", "  _
  (" & Format(Now, "yyyy-mm-dd hhmm") & ").xlsm")
End Sub

But this code doesn't run at all. I get Error 1004 every time I close the workbook:

Private Sub Workbook_BeforeClose(Cancel As Boolean)
  ThisWorkbook.SaveCopyAs (ThisWorkbook.Name & Format(Now, "yyyy-mm-dd hh:mm"))
End Sub

The message I get when trying to close the workbook with the second code: http://prntscr.com/8iiyyd

It is the colon that prevents Windows from saving the file, plus the extension will be strange with the timestamp added like this. Your code would produce the following filename: Try.xlsm2015-09-22 15:37

You will also need to supply your folder location.

Maybe you can try this:

ThisWorkbook.SaveCopyAs "c:\folder\" & Replace(ThisWorkbook.Name, ".xl", Format(Now(), "yyyy-mm-dd hhmm") & ".xl")

You can of course specify your own folder.

If you want to put it in a subfolder, relative to the current file location, then use this:

ThisWorkbook.SaveCopyAs Thisworkbook.Path & "\subfolder\" & Replace(ThisWorkbook.Name, ".xl", Format(Now(), "yyyy-mm-dd hhmm") & ".xl")

You can of course specify your own subfolder

Hope this helps