You can clone your drive to the external via the command line (that's what you're booting into), type this:
sudo rsync -avrogx / /Volumes/[Backup Volume]
Where instead of typing [Backup Volume] type the name of your backup, if it's more than one word, say it's called "Backup Volume, instead of typing:
sudo rsync -avrogx / /Volumes/Backup Volume
type instead:
sudo rsync -avrogx / /Volumes/Backup\ Volume
If your volume is just one word, say "Backup" then that's easy, just type
sudo rsync -avrogx / /Volumes/Backup
Should be a piece of cake.