You can put up a picture as your profile picture. Then later you can replace it with a different photo, or with a generic avatar. In either case, your old photo goes away. You can do the same with your cover photo. If you are talking about a picture in the body of a question or opinion, you post a link to your picture at another site like imgur. All you need to do to remove it from G@G is to delete it from the photo hosting site (imgur).