I had a similar problem...sometimes is actually in your set up. Deep divots are caused by an extremely steep arc in your swing. What can cause this is a set up where for example your feet are lined up to the right of your target and your shoulders are pointed at the target. In essence your body is crossed up and swinging against itself. Try lining up your shoulders to point the same direction your foot line is pointing and make your swing path correspond with that line.
If that doesn't cure it, try backing away from the ball a little and flatten your swing plane out.