Photo Stream is a convenient feature in iCloud that enables Apple users to upload and store photos taken within 30 days, as well as to push up photos to all your iOS devices. In fact it is more like a "push up" function than a synced process. As long as you turn on Photo Steam by "Settings"→ "iCloud"→"Photo Steam", all the new photos hereafter you have taken will be uploading to iCloud as well as being automatically pushed up to your other iOS devices'Photo Stream folders.
Photo Stream restored in iCloud will remain even though you delete Photo Stream on your iOS devices. Then how shall we completely remove Photo Stream from iCloud?
1. Log in to your iCloud account on www.iCloud.com.
2. Click the account name in the upper right corner.
3. Click Advanced > Reset Photo Stream from an automatic popup window.
4. Click Reset and make sure if you really want to reset Photo Stream.
5. You have to log in again to finish confirmation.
6. A popup window shows that all your photos on Photo Stream have been deleted from iCloud.
7. Go to Settings > iCloud > Photo Stream, turn off My Photo Stream and Shared Photo Streams. Now all the photos in Photo Stream have been thoroughly removed.
Notice: Even though you turn Photo Stream on again from your device, there won't be any auto-loading old photos on iCloud, which means that you have completely deleted photos from Photo Stream.
Now your Photo Stream will be reset and all photos removed.