If you've already examined the autorecovery files in ~/Documents/Microsoft User Data/Office 2011 AutoRecovery and there's nothing, you're out of luck. "Time machine" is a built-in backup tool that works with your Mac and an external drive, As the problem you described, I read it. The files deleted in Trash bin could be a different problem which Time machine can't solve. you can read this article and learn more. I hope it will help.

The first thing you need to do is going to try your external drive on different computer to see if the drive can be read by them. If yes, back up the files you store on your external drive to the computer first. If not, you need to take your external drive to fix at once. Maybe you will ask if you fix the external drive, will the files are gone forever? Yes, they will be gone, but not forever. Actually, after fixing the external drive, the files seem to be deleted, but in fact, the operating only delete the catalog and the space of these files so that there is enough space for you to store new files.At this moment, you still have chance to get your files back. But if you put any new files into the external drive, the new files will occupy the space of the"deleted files", this is the so-called data overwritten situation.Once this happens, you may lose the chance to get the files back.

The first thing you need to do is going to try your external drive on different computer to see if the drive can be read by them. If yes, back up the files you store on your external drive to the computer first. If not, you need to take your external drive to fix at once. Maybe you will ask if you fix the external drive, will the files are gone forever? Yes, they will be gone, but not forever. Actually, after fixing the external drive, the files seem to be deleted, but in fact, the operating only delete the catalog and the space of these files so that there is enough space for you to store new files.At this moment, you still have chance to get your files back. But if you put any new files into the external drive, the new files will occupy the space of the"deleted files", this is the so-called data overwritten situation.Once this happens, you may lose the chance to get the files back.