Sending a HTTP DELETE to the Atom representation of a permission will remove it completely. Please note: there is no undo and this is a single-step process; once permissions are removed they are deleted for good - if you delete permissions on a folder, this will cascade through to all sub-files and sub-folders. We do not need to send any extra content with the DELETE.

mat@augustus:~$ curl -i -X DELETE -u cuscav
   "https://files.warwick.ac.uk/files/api/atom/permission?account=mmannion&path=mmannion%2FFiles%2F&permission=ff8081813fcd8ee6013fcd9198f40002"
Enter host password for user 'cuscav':

HTTP/1.1 200 OK
Date: Thu, 11 Jul 2013 12:04:34 GMT
Content-Length: 0
  

No content is returned in the response body for a DELETE.