The new iCloud Photo Stream feature makes it easy to access your photos on any device. It doesn’t allow deleting of individual files, but you can clear the entire stream. Here’s how.
First head to iCloud.com and log in with your Apple ID. Click on your name.
The Account screen comes up. Click Advanced.
Click Reset Photo Stream. Then click Reset to the verification box.
After clicking Reset, you’ll get a confirmation message. Click OK.
Then to delete the photos from the Photo Stream section on your device(s), switch Photo Stream to Off. To do this go to Settings >> Photos.
Tap Delete Photos. After deleting the photos, you can turn Photo Stream back on again and start sharing new pictures.
Resetting your Photo Stream is handy if you upload pictures you don’t want shared on your device or to simply save space.