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?
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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.