I cloud

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 → Optimise Storage on your mobile device and Photo Preferences → iCloud → 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.

In most cases optimising your photos should be enough to alleviate space related issues on your device. If however, you have an exceptionally large library you may need to turn off iCloud photo library on your mobile device and use photo stream instead. You can then use a computer to handle photo stream photos and have them automatically imported into your iCloud photo library. If you don’t have a computer, you can still access photo stream from other devices that don’t use iCloud Photo Library and import the photos directly to that device.