Extreme Weather Mitigation Act of 2013 - Directs the Secretary of the Army to give funding priority to authorized projects and studies with a primary purpose of hurricane and storm damage risk reduction that: (1) address an imminent threat to life and property, (2) prevent storm surge from inundating populated areas, (3) prevent the loss of coastal wetlands that help reduce the impact of storm surge, (4) protect emergency hurricane evacuation routes or shelters, (5) prevent adverse impacts to publicly-owned or funded infrastructure and assets, (6) minimize federal disaster relief costs, and (7) address hurricane and storm damage risk reduction in presidentially-declared major disaster areas.

Provides for expedited consideration of previously authorized water resources projects that meet such criteria.

Sets forth criteria for prioritizing new studies for hurricane and storm damage reduction.