Backing Up a Macbook Air

Right now my Macbook Air is almost out of storage space. I have over 100 gig available on iCloud. I can't seem to be able to move over all my photos (10,000+). That's one problem. The other is this: I have an external hard drive also. If I back up all my photos on the external, can I then go ahead and delete the photos on my Mac? Or does the external drive just mirror the Mac, meaning if I back up the photos and delete them from the Mac, they'll disappear from the external drive, too? I'm lost. Any help is appreciated, thanks!