Some of the ideas being proposed will definitely work to make a of files from one drive to another, but for your particular purpose may not meet you needs. For example, using a backup utility only works over a few hours unless you have it backup every 5 minutes (and then it can be a nuisance in terms of computer resources). If you edit your files and then shut down your computer there is no guarantee the most recent version is on the external device. You need something that will constantly be checking the file status to see if it has been modified and then make a copy of that modified file to a destination.
Conceptually this is a simple task, but actually implementing it may not be so easy, involving scripts. The easiest would be to simply make an alias of the file so you are working off a single copy on the hard drive. An alias on your computer makes a pointer the files actual location on the external drive. Or for that matter, if you always have this drive attached, why not simply open it from its location on the external drive. I have 4 drives attached to my computer and I can open a file on any of them.