You can use AppleScript to do that. The following will do what Fishrrman previously mentioned:
tell application "System Events"
try
set the clipboard to ""
on error err_message
display dialog err_message
end try
end tell
Call this after you finished copying&pasting your data. Otherwise: why don’t you just simply drag&drop the text from one window to the other (putting them side by side or CMD-Tab between them? Your using a Mac. I know this is old school ?, but this will leave nothing in the clipboard.
EDIT:
Also, Automator allows the same. You'll need to define a variable, double click on the name text to set it to null, and then drag in the set clipboard action before running / saving it. The benefit of using automator is that you can assign it as a service and then use system keyboard shortcuts to call it.
if you copy always to the same program you can automate this service further e.g. you only have to select the text and it is automatically added/appended to your new document so you don’t even have to switch to the other program, etc....