Can't Delete Time Machine Backups, Can't Move Them Out of Trash
So, as an answer, save any other data on another drive, then reformat and partition the drive.

You shouldn't be able to put any Time Machine files into the trash in the first place, so if that happened, you need to get anything you care about off that drive and erase it anyhow. If you don't need the backups - you can use Disk Utility to just erase the drive - that will empty your trash instantly as well as all the data on that drive.