A well-timed Sadism can bait enemy champions into attacking you even when they lack the damage to finish you.
Spirit Visage will increase the healing done by your ultimate and lower cooldowns on all of your abilities.
Cleavers are a powerful tool for killing neutral monsters. Instead of returning to base, farm neutral monsters until your ultimate can heal you.
Try to coordinate high-damage abilities with your allies right after Dr. Mundo uses his ultimate, but if you're unable to kill him quickly with burst he will heal through the damage.
Try casting Ignite when Dr. Mundo uses Sadism to negate a large portion of its healing.