Sounds like you have a shortcut to the document on the desktop, not the document itself. Did you try putting the external drive back in and opening it again?
File recovery can be tricky some times. There are several options one can use like recuva or PC Tools for windows. You can get some other freeware and or open source downloads at sourceforge..net. Also check out file recovery options at Analysis and Review dot com
Based from your stated problem, you might not have saved your word document before you unsafely remove your external hard disk drive. Unfortunately, there is no option to recover your unsaved document. The best thing you can do is to create a new document again and carefully and surely save your documents in both desktop and external hard disk drive.