The meaning of mitigate is straightforward enough: it is most often used to talk about making something, such as a problem, symptom, or punishment, less harsh or severe. Sometimes, however, it appears where the similar-looking militate is expected. That word, which is often followed by against, means "to have weight or effect," as in "your unexcused absences might militate against your getting a promotion." The two words are not closely related etymologically (mitigate descends from the Latin verb mitigare, meaning "to soften," whereas militate traces to militare, another Latin verb that means "to engage in warfare"), but the confusion between the two has existed for long enough that some usage commentators have accepted "mitigate against" as an idiomatic alternative to militate. If you want to avoid criticism, you should keep mitigate and militate distinct.

mitigate or militate?

Would it be correct to say, "His boyish appearance mitigated against his getting an early promotion"? Most usage commentators would say "no." They feel such examples demonstrate a long-standing confusion between mitigate and the look-alike militate. Those two words are not closely related etymologically (mitigate descends from the Latin verb mitigare, meaning "to soften," whereas militate traces to militare, another Latin verb that means "to engage in warfare"), nor are they particularly close in meaning (militate means "to have weight or effect"). The confusion between the two has existed for long enough that one commentator thinks "mitigate against" should be accepted as an idiomatic alternative to militate, but if you want to avoid criticism, you should keep mitigate and militate distinct.