Removing photos off iPhone 14 Pro Max

You would need to turn off iCloud syncing. iCloud Photos is a synchronization service. When you engage iCloud Photos on a device, then the Library on that device is kept exactly the same as the iCloud Photos Library.  So if you want them to have different stuff, then they can't be connected. If you reconnect later, then all the pictures on the phone will be sent to iCloud.com, and all the pictures there will be copied to your phone. If you delete a picture on your phone, then that picture is deleted at iCloud and on all the other connected devices. 

So you can't think of iCloud Photos as a separate storage place, and you can't think of it as a backup service, since it backs up mistakes, and there's no way to undo them. While it is connected, whatever you do with Photos on your device-- it happens everywhere else.