Can I REPAIR my External Hard Drive in Disk Utility without losing all of the Data?

So, here's the story...

A while back, I made the mistake of throwing my TM backups in the Trash folder. They were "stuck" there in my External Trash FOREVER until I finally decided to do something about it. I read a few forums that gave instructions on how to delete those volumes through Manually through a series of prompts in TERMINAL. This process actually WORKED and removed the files from the trash, HOWEVER, now the Disk isn't mounting properly. After running "Verify Disk" in Disk Utility, It's telling me that the disk needs to be repaired.

Fearing that my disk may be wiped completely, I thought I'd transfer all the files over to another HD and Repair the Problematic Disk just to be safe.

But When I try to copy the files over to another drive with ample space, it gives the message "The operation can’t be completed because the selection contains both backup items and non-backup items."

I am now at a cross roads, because I DO NOT WANT TO LOSE ALL OF THE DATA ON THIS DRIVE!!!! What do I do??