For people who are still having issues with this, and who have the simple clipboard feature that only remembers the last thing you copied: the easiest way to get rid of the previously copied item to the clipboard is to copy something else to the clipboard. This will automatically get rid of what was copied there previously, because the basic clipboard function will only remember the last thing you copied.
If you don't want anything at all in the clipboard, then try typing 3 or 4 blank spaces in a text field, then select those spaces (just like you would a word), and select Copy. This will copy the blank spaces to the clipboard. Anyone who tried to paste what's in the clipboard would just be pasting a few spaces.