I deleted backup files from an external drive that is hooked up to my iMac. The folders now sit in the trash can on Mac. No matter what I do it can not be deleted from trash. I either get a message: The Operation can not be completed”

As den.thed says, they shouldn't be showing up from a disconnected drive.

In Finder's Menu, select Go menu>Go to Folder, and go to "/volumes". (no quotes)

Volumes is where an alias to your hard drive ("/" at boot) is placed at startup, and where all the "mount points" for auxiliary drives are created for you to access them. This folder is normally hidden from view.

Drives with an extra 1 on the end have a side-effect of mounting a drive with the same name as the system already think exists. Try trashing the duplicates with a 1 or 2 if there are no real files in them, and reboot.

If it does contain data...

http://support.apple.com/kb/TS2474

If your TM drive is disconnected, then I would suspect that it is another folder or file that is stuck in the trash.

see > If you can't empty the Trash on your Mac - Apple Support

Ah, no idea why Apple hasn't fixed this, you deleted things from the TM in the Finder instead of in Time Machine itself.

The only way out is to erase the TM drive & start over.

Yes, it will empty it by reformatting it.

In fact if you disconnect the drive the Trash will show empty, because each drive has it's own trash.