To mitigate means to lessen the severity of an offence or mistake or to make something bad less severe, harsh or painful. 

1. My work comes with a lot of stress, so to mitigate that I make sure I give myself time to unwind.
2. The student grant helped mitigate some of the costs of returning to education.

1. Senior figures at the company are currently trying to find ways of mitigating the heavy losses they made last year.
2. The high cost of the refurbishment of the shop premises is mitigated by the likely increase in turnover that will result from it.