Suppose you contract with someone to shingle your roof. Because the roofer botches the job, breaching the contract, rain leaks into your house. You can assuredly win damages for the value he has denied you, the cost of repairing what he has done improperly, and probably the initial damage caused by the leak. But you cannot stand around watching water flood your house and expect to recover for all the harm thereby wrought. You have a "duty" to take reasonable steps to mitigate your damage, such as by putting a bucket under the leak. You'll suffer no punishment if you fail to so mitigate, of course—hence the scare quotes—but neither can you make the roofer pay the price of your laziness.
Shame on me for writing so obscurely!