How come files get deleted from the iOmega backup hard drive when I only want them deleted from my Mac Mini?

I am trying to set up Snow Leopard onto my Mac mini, but there is not enough space on the hard drive. So I backed up (with Time Machine) everything on my hard drive onto my iOmega mini max hard drive. I then selected three videos that are all on the Mac mini and the iOmega and dragged them to the Trash, only to have the files delete not only from the Mac mini, but also on the iOmega. I have to delete lots of files on the Mac mini to make room for Snow Leopard and I don’t want them deleted off the back up hard drive too.