You may reset your Photo Stream by logging into your account on icloud.com. Resetting removes all your Photo Stream photos from your iCloud account. However any photos that have already been streamed to your other devices will not be deleted. Here is how you can do it:
- Visit icloud.com and login to your account using your Apple ID credentials.
- Click on your name.
- Click Advanced.
- Click Reset Photo Stream.
Once you reset, it cannot be undone.