Backing Up Macbook Pro, then Erasing.

My macbook pro is getting way to crowded and I have been backing up and erasing what I can but I still can't erase enough. I was wondering, is it possible to back it up on an external hard drive then eject the hard drive and completely erase the laptop but still be able to access the files that I had before on the external? I kind of know the answer to this I just don't want to go an erase my laptop without having someone that knows this stuff more than I do confirm that it will be okay.

Copying files to an external drive and then deleting them from your internal drive is NOT "backing up" those files.
You are essentially "moving" those files to a new location.

As soon as you delete the files from your internal drive, the external drive is no longer a "backup" drive, it is has become a "data storage" drive.

If that data only exists on that single external drive, you do NOT have a backup.

If you "completely" erase the internal drive, how are you going to start up the computer? Since "everything" including the operating system will be gone...

What Mac do you have?
What size drive is in it? include amount of used and free space.
What version of OS X are you using?
What type of files are you wanting to move from the internal drive and store on an external? Apps, games, movies, music,, etc.?

To use an external drive as data storage, you will need another external drive to backup both your computer and the external data.