Hi Jon
Are you talking about GarageBand or LogicProX? (You are in the Logic Pro forum)
By default media files you create while recording are placed in User/Music/GarageBand(or Logic)/then whatever the title of the song is.
After connecting an external hdd you can select all the files you want to copy or even the entire folder and drag to the location you want in the external hdd. This will copy the files. If you want to move the files without first checking them you can hold down the "Command" key. This will erase the files after moving to the other disk. Use caution here as you cannot recover the files.
You can then delete any files you want by moving to Trash and emptying. This will free up the space. You will not gain any space until you empty the Trash.
You can also use the standard copy and paste if you want to go that route.
I very strongly recommend that you have back-ups before doing any of this.
Hope this helps, Greg