If iCloud Photo Library feature is on, then no. iCloud acts like a hub to keep all your devices connected to your Apple ID synchronized. That's the main function of iCloud actually. It stores your data (some of it in specific folders and apps, not everything) and allows you to access them all on any device. If you manage that data (add, delete, rename, move, etc.) in those devices, it'll then be replicated to all others. That's what iCloud is for.
To do as you asked with your photos you must deactivate iCloud Photo Library, so you'll be able to freely manage your photos, but it'll stop doing things automatically and you'll have to copy/move them to any place you want them, just like the old days.
More about it all:
Set up and use iCloud Photos - Apple Support
Get help with iCloud Photos - Apple Support
Manage your photo and video storage - Apple Support
Optimize storage space on your Mac - Apple Support
And inside those articles you get a number of other links that'll teach you even more.