Delete Photos

Do you have the iCloud Photo Library enabled on your iPhone and Mac? If so you can't as the iCIPL is a syncing feature and any change, i.e. deletion or edit, made on one device will be mirrored on all devices.

If you sync your photos with the My Photo Stream and your Photos/iCloud preference pane is set up like this:

You can delete the photos from the Camera roll on your iPhone and they will remain in the Mac's library.

All you have to do is back up the photos on mac, then you should be fine if you delete them on mac. You can also delete both photos then recover the photos on mac, and then fully delete them on your phone.

If you have iCloud/syncing enabled, you will lose them all.