This question comes up occasionally. While you can turn off automatic saving in SC (see the Miscellaneous Tweaks tab), it's not what I recommend, and if you copy stuff to the clipboard SC may insist on saving it first.
However, a better solution is to go to the Saving and Loading tab and tell SC to Auto Move Older screenshots and have it auto file old screenshots into an OLD folder if they are older than 1 day. Then you can just delete that folder from within SC whenever you feel like it.