It should be noted that using an external drive as scratch disk is a very suboptimal solution. It is vastly better if you can manage to clean out your system drive to use that, at least as primary scratch with the external as secondary.
Use the external to dump everything you don't need to have on your system drive. Then run disk cleanup.
I don't know how big your system drive is, but as a general guide, your operating system and program files should not take up much more than around 100GB. If you have significantly more than that, it pays to do a thorough housecleaning. An incredible amount of junk tends to build up in your user account over time.