I just ended a week of struggling with this. I had 60GB of files in my 200GB on iCloud. I found them impossible to delete, in Finder, or in the online ICloud. I could delete a file or two, maybe a small folder, but 60GB would be months deleting that way.
I chatted and emailed and called Apple. They had numerous people call me over a week, and couldn't help. I told them to please just delete every file on my ICloud account, I have backups, but they couldn't do that.
I'm an Electrical Engineer with a computer science focus, this isn't scary or strange to me, Apple's file management software, on the laptop and online simply did not work.
Finally, after multiple calls and HOURS on hold, the 3rd or 4th guy called, from a 512 area code (Austin TX). He clearly didn't understand and tried to BS his way through it. Like I said, I know this stuff, I have a 163 IQ and WROTE an OS for fun in college. This nitwit talked in circles for an hour, while I challenged everything he said - since I'd been working on this with people from APPLE for a week and we really had tried everything He told me ICloud can't handle large files, many files, or backup files, though it is specifically designed for backup files. He told me ICloud file manager couldonly handle deleting 30 files at a time - now THAT was probably the only truth he said, Apples file manager software *****. I decided to have some fun so I pointed out that my 60GB was an average of 20KB files. Online ICloud file deletion runs at about one file a second. To delete my 60 GB - not including changing folders - would take 3 MILLION seconds, or about 35 days of me sitting in front of the machine. Now what about those poor fools who bought - and FILLED - a 1 TB account, they would have to spend 18 MONTHS deleting files 30 at a time. The fool just started spouting the same confusing BS, I tired of talking to a nitwit, and hung up.
I decided to cancel my account, drop back to the free 5GB, then Apple would be FORCED to delete my 60GB of files.
Given the normal high quality of Apple support, this was very disappointing
Today I drove to town where my iPhone works and lo and behold, in iCloud on the iPhone I could delete all data files WITH ONE BUTTON - AND IT NOT ONLY WORKED, IT TOOK ONLY 30 SECONDS TO DELETE EVERYTHING.
So, the moral of the story is don't use iCloud to store computer files unless you have an IPhone, as only an IPhone can manage computer files stored on ICloud.
It's very unsettling that this IPhone method works so well, and nobody at Apple who gets the calls about deleting ICloud files knows this method. I just wasted 7 days and 4-5 hours on the phone to multiple Apple support folks, none of whom knew this IPhone method. I just upgraded to IOS 8.4.1 and maybe this is a new feature???? who knows - Apple sure doesn't.
Clearly, Apple has a lot of work to do before ICloud can be used for anything but sharing keychain and a few application files.
For those interested in online Cloud storage, I also have Google Drive and SkyDrive. Google Drive works, but is a bit cumbersome. SkyDrive works just like you would expect it to work. I can copy or erase 60GB over a very slow connection, and it takes forever, but works flawlessly and maybe more important, keeps me informed how it's doing.