If you click the Delete button in the Resource Manager you will remove any files that are currently selected with a checkmark in the leftmost column of the list. These files will also disappear from Live Sites. You should make sure that a file is not being linked to or displayed on a Live Site before you Deleteit.
*** DANGER ***
THERE IS NO APPROVAL PROCESS FOR THE DELETE FUNCTION.
IF YOU CLICK "DELETE" YOUR FILE IS REMOVED FROM THE CMS.