I often cut + undo because seeing the cut is feedback which tells me the operation successfully put the content into clipboard. This is not always a guarantee especially in web apps, and sometimes I just have focus on the wrong window.
Have you used a clipboard manager? There are tons that you can configure with notifications and indicators, so you don't have to that.
How can you be sure that the undo stack is in sync with the clipboard? Wouldn't cut+paste be a more reliable pseudo-copy than cut+undo?