Your phone is automatically syncing them to the cloud and that's a good idea because the cloud is your backup. So you want to have your computer stop grabbing them from the cloud. Open System Preferences and select iCloud. Click off the checkmark next to Photos to completely disconnect your computer from iCloud. You'll be asked if you want to delete Photos from your computer and it sounds like you do.
Now the downside to this is that if you should have a photo on your computer (maybe you downloaded it from a site or got it in email) and you want it on your phone it won't automatically go there. For those you can use AirDrop, email them to yourself, or log onto iCloud and move them onto your cloud Photos which will sync them with your phone.