Ctrl+C > Ctrl+V > Backspace is probably better than the accepted answer due to fewer key strokes. I know this doesn't really answer the question, it sounds like your question is really a feature request. As mentioned in the comments here is a macro solution as well:
Sounds like too much work to me to avoid a backspace key stroke. If it's large grabs and pulls, I would just suggest using Notepad++'s advanced find/replace and exploit the
\n\r\t characters that are the real text appended to the copy/paste and replace them with nothing.