I haven't enabled copy/paste or cut/paste, but you can drag shapes between diagrams.
To show multiple diagrams, either use the Diagram Spy window for your drag source/drag target or open multiple windows. To get two diagrams from the same model side-by-side, choose Window/New Window then right click on the tab of the new window and choose New Horizontal Tab Group.
You can find additional information on window management and the Diagram Spy window in the Window Management in Visual Studio and General Use sections of the Readme.htm file that installs with NORMA in the Documentation directory of the install location (C:\Program Files\ORM Solutions\ORM Architect for Visual Studio 200n\Documentation).
PS By default, the 'Ctrl-Delete' key deletes the underlying element from the model and 'Delete' deletes the shape. I generally switch these bindings in the ORM Designer options page. To switch:
Select the Tools/Options menu.
Select the ORM Designer section to the left of the Options dialog.
Find the Delete Key Behavior in the Delete Behavior section on the page.
Choose DeleteElement instead of DeleteShape.