Greetings,
A backup is a copy of the original file so you have 2 copies (The original and the backup). If you use TimeMachine to backup your computer and then delete the original files from the computer you don't have a backup, you've just moved the file from point A to point B. This is not what TimeMachine is for, and more importantly, its more work than you need to do.
If your goal is not to backup but rather, move files off your computer, just drag those files to the drive to copy them, and then delete the original. This will free up the space and leave the copy on the external drive.
I would suggest moving single large files if at all possible (like movie files).
Note: Before you start moving files to an external drive make sure that drive is mac formated.
Cheers.