Deleting back up files

Open Disk Utility. In the list on the left find your Time Machine backup drive. This image shows what this looks like on my system:

I have selected the out-dented entry for my Time Machine drive as you can see above. Click on the Erase button in the toolbar. A panel will drop down like this:

Be sure that you set your Format: and Scheme: selections exactly like above. Then click on the Erase button in the panel. That's it. Disk Utility will now erase the selected drive.

If you click on the little downward arrow on the bottom left of that panel it should then show you why it failed. Quit Disk Utility. You should turn off Time Machine if it's currently enabled. I would then eject the Time Machine drive. After it is ejected disconnect it from the computer. Wait ten seconds then reconnect the drive. After it mounts on the Desktop open Disk Utility and try erasing it once more.

You must remove old files from a Time Machine backup drive using the Time Machine application. What you have done will either take weeks to complete or simply won't ever complete until you reformat the backup drive which is what I recommend doing. Afterward, you can perform a new backup.

Drive Partition and Format - El Capitan or Later

1. Open Disk Utility in the Utilities' folder.
2. After Disk Utility loads select the drive (out-dented entry with the mfgr.'s ID and size) from the side list.
3. Click on the Erase tab in the Disk Utility toolbar. A panel should drop down.
4. In the drop down panel set the partition scheme to GUID. Set the Format type to Mac OS Extended (Journaled.)
5. Click on the Apply button and click on the Done button when it is activated.
6. Quit Disk Utility.

It would be the entry above the one you have selected. Macintosh HD is IN-dented. It sits below the one that is OUT-dented. Below this is another out-dented entry for the second drive which is a Samsung.