The Clipboard is the magic place where Copy and Cut stash selected things, and Paste takes the Clipboard contents and puts it in at the insertion point.
"Show Clipboard" is provided as a convenience to you to VIEW, but not manipulate the Clipboard. You cannot, by definition, copy or cut or paste in the "Show Clipboard" window, since it is showing you what is already on the clipboard, and it will not edit anything there or do recursion.
You need to find a new destination (such as a new TeachText document) and Paste the contents of the clipboard there. At that point, you could select a subset and copy or cut. (Another way is simply to select a smaller amount of stuff before you cut or copy.)
When the contents of the Clipboard gets too large, or when you switch Applications between Cut and Paste, the contents of the in-memory Clipboard is often stored in the Clipboard File inside the System Folder.
Drag and Drop was introduced very late in the development of OS 9. It may not be available AT ALL in 9.0.4. You should see if you can get it done using only Cut/Copy and Paste.