Delete photos from one device only

To elaborate a bit on picas's advice: When you delete photos from a device, that is syncing with iCloud Photos, the photos will be deleted from iCloud and all other devices syncing with iCloud Photos as well. iCloud Photos is keeping the photos on all devices identical to the photos in your iCloud Photos Library. To be able to have different or less photos on the old Mac, disable iCloud Photos o the old Mac, but keep it on on your other devices. However, after you disable iCloud Photos on the old Mac, you can no longer access the iCloud Photos on this devices with the Photos.app. You will be restricted to the web interface at www.icloud.com .

Turn off iCloud for Photos.

Good Luck, Roo_bear!