i am out of space and cannot back up or export files

You haven't posted a question for us but I am going to assume that your objective is to be able to export some files to an external disk so you can clear up needed storage on your Mac.

1. Being out of space is a serious problem. Yes, that means that you cannot update or upgrade your computer's operating system. It also means that you may be at risk of your computer locking up and no longer able to be used. If that happens, you will have a real problem.
2. Yes you can backup. To do so you only have to use Apple's Time Machine app and have a dedicated external backup disk to backup to. Do you have one? Ideally it should be two or three times as large as the amount of data being backed up.
3. Yes you can export files. Again, you need a different external disk to export to. Copy the files you want to export by dragging them over to the external disk. Then you can delete them from your hard drive to clear needed space.
4. So, you will need two separate external disks. Do you have them? If so, what is preventing you from using them as described above?