For the low punch shot, you need to tilt your spine and head towards the target at address. This means setting your weight on your left side at address and pushing the ball back in your stance so it is opposite your right heel. Choose a club without much loft and using this set-up position you'll lower the face angle even more.
Instead of making a long, flowing swing, you need to produce a more truncated action. A fast clubhead speed will create more spin on the ball - and spin makes the ball fly higher. So use a short backswing, keeping your technique solid and under control.
A shortened finish position will automatically reflect that truncating backswing. Don't make a long release through the ball, but hold your hands at waist height. Keep your head fairly still and watch the ball fly low towards your target.