It’s not as good as selectively being able to remove images, but if you’d like to clear out your iCloud Photo Stream, it only takes a few clicks.
First, you’ll need to log into [iCloud](https://iCloud.com) from a traditional computer. If you get taken straight to the last app you used at the site, back out to the main app screen (the one with the iOS-like icons for Mail, Contacts, Calendar and so on), and click on your account name in the upper right-hand corner.
Once the profile popup is available, click “Advanced” and you’ll be presented with the option to clear your Photo Stream.
Make sure you’ve saved whatever images in your Photo Stream that you want to keep, or check to see if they’re still in the Camera Roll of the device you shot them with. There is no way to reclaim your Photo Stream images once you delete them this way.