Photos on the cloud
How do I prevent photos from being deleted from my cloud when I delete them from my phone?
MacBook Pro with Retina display, iOS 9.0.2
Welcome to the Apple Community.
With iCloud Photo Library enabled, you cannot delete a photo on one device (or at iCloud.com) without deleting it from every device that uses iCloud photo library (and iCloud.com). In order to save space on your mobile devices (and indeed your Mac if you wish to do so) turn on optimisation for photos on these devices (settings > photos & camera > optimise storage on your mobile device and Photo preferences > optimise storage on your Mac)
Optimisation is dynamic, it reduces the resolution of your photos as and when needed, so you may not notice it occurring at first. However when it is needed, it is very effective and users have reported libraries being optimised to much less than 10% of their original size in some cases. My own library is about 9% of its original size on my phone.