According to the United States Census Bureau, the township has a total area of 34.0 square miles (88 km2), all land.

Southwest Township is located in the southwestern corner of Warren County in the Pittsburgh High Plateau.

The highest elevation is 1,762 ft (537 m) at the northeastern part of the township, approximately 0.5 mile west of Excelsior Corners, Pennsylvania.

The racial makeup of the township was 99.11% White, 0.36% African American, 0.18% Asian, and 0.36% from two or more races.

23.2% of all households were made up of individuals, and 6.8% had someone living alone who was 65 years of age or older.