http://support.apple.com/kb/HT4486
iCloud: Photo Stream FAQ
How do I delete photos from my Photo Stream in iCloud?
Individual photos cannot be deleted from your Photo Stream. You can, however, delete all the photos in your Photo Stream by clicking the Reset Photo Stream button in your account at icloud.com. The Reset Photo Stream button will instantly delete all Photo Stream photos stored in iCloud, but it will not remove any Photo Stream photos that have already been pushed to your devices.
How do I delete photos from my Photo Stream on my devices?
After deleting the photos from your Photo Stream in iCloud, you can remove the Photo Stream photos from your devices as follows:
On your iOS devices, go to Settings > iCloud > Photo Stream and turn Photo Stream off. This will delete all the photos from your Photo Stream album. If there are any photos you want to keep on your device, make sure to add them to an album or save them to your Camera Roll first.
On your Mac, go to iPhoto or Aperture preferences and turn off Photo Stream. This will delete all the photos from the Photo Stream view. If you had Automatic Import enabled in Photo Stream settings, your photos were also imported to your iPhoto or Aperture Library and will remain after you disable Photo Stream. If you want to delete any of these photos from your Library, you can do so manually any time you like.
On your PC, you can remove Photo Stream photos by deleting them from your designated Photo Stream download folder. By default, this folder is located at
C:\Users\Apple\Pictures\Photo Stream\My Photo Stream.