How do I delete photos from my Mac without deleting from iCloud?

As the others have pointed out iCloud synchronises the libraris accross your devices. What is on one is on all, what is deleted from one is deleted from all.

If you are looking to save space on your mac (is that what you are trying to do?) then you have three options.

1 - Disable iCloud photos. Then you can delete what you want on your mac without affecting iCloud and your other devices. But then you need a new way to transfer pictures to your mac.

2 - Move the library to an external drive:

See

https://support.apple.com/en-gb/HT201517

3 - Turn on "optimise mac storage" Then the full size masters are not stored on your mac - only thumbnails and previews. This can dramatically reduce the space taken by your library, and full size masters are downloaded only when needed, eg to edit or export. Bear in mind if you set this, then masters are not moved from your mac immediatly - only when it is running out of space.

If you are using iCloud photos then whatever you delete on a device will be also gone from iCloud and there is no easy way around it. You could export the photos in question and store them somewhere els e.g. an external storage.

apfelkopf is correct. You may not realize that iCloud is NOT a backup site. It mirrors what is in your computer and is designed for sharing among your devices. If you are relying on iCloud as your backup, don't.