Slug Your Slice
I like to study the golf swing in biomechanical terms, but for you it's better to have an athletic feel. Consider boxing: You want to swing with a tight uppercut motion (above, right), not a looping hook (left).
Players who slice throw their hands out and around on the downswing and leave their hips and lower body behind. Instead, thrust your belt buckle up and toward the target through impact--as your right shoulder turns through lower than your left--like an uppercut to the chin. Your upper back will tilt slightly away from the target at the finish. You might top a few shots at first because you're changing your swing shape, but you'll learn to hit a draw in no time.