General:
* Alleviate
* Reduce
* Lessening
* Diminish
* Abate
* Ease
* Moderate
* Soften
* Counteract
* Allay
Formal:
* Ameliorate
* Palliate
* Attenuate
* Assuage
Specific:
* Mitigate risk: Control, Manage, Minimize, Limit
* Mitigate damage: Repair, Restore, Remediate
* Mitigate suffering: Comfort, Soothe, Console
The best synonym will depend on the specific situation and the intended meaning.