A single diagram item or a selection of items can be copied or cut to the clipboard. This is done programmatically using the CopyToClipboard and CutToClipboard methods. To paste the clipboard contents into the current diagram call PasteFromClipboard.
MindFusion.Diagramming does not provide keyboard interface to clipboard operations. You might assign the standard CTRL+C, CTRL+X and CTRL+V shortcuts to menu items and handle them by calling the respective methods.