First, save all photo's you want to keep in the stream to your library in iPhoto > go to icloud.com > log in and click your name in the top right > Advanced > Reset Photo Stream > then turn photo stream off and on again on all your devices > to add the photos you do want, drag them from your library into Photo Stream using iPhoto again.
Hopefully Apple will implement a simple way to delete just the photo's you don't want in a future update.