Against drmundo, Dr Mundo can farm really easily under his tower. Try to not have the lane pushed against him because it actually benefits him. Instead, keep the wave even or closer to your side of the map so you can receive ganks.

If Dr Mundo is behind, he will start farming with his Q. Do not get in the way of them unless he is trying to secure a Cannon Minion.

Dr Mundo is rather immobile and can easily be killed when locked down. Request assistance from your Jungler to execute him when he is low. Against drmundo, Dr. Mundo can very easily grow under his turn. Try not to push the way against him because it is really beneficial to him. Instead, keep the wave even or closer to your side of the map so that you can receive ganks. If Dr. Mundo is behind, he will start cultivating with his Q. Don't start there unless he tries to secure a Minion Cannon. Dr. Mundo is rather motionless and can easily be killed when he's locked up.