Born in Pennsylvania, Stevenson started his career as a cabinet maker and later moved to Wood County, where he became a farmer. During the Civil War, he was a strong Union supporter. While advocating for the cause, he was indicted by a Parkersburg grand jury for "circulating an incendiary document entitled Helper's Impending Crisis." He never went to trial.

He helped write West Virginia’s first constitution and served in the state senate before becoming the state's third governor in 1869. As governor, Stevenson pushed for better roads, education for Black citizens, and restoring voting rights to former Confederates. This led to Democratic control of the state for decades. After losing re-election, he worked in journalism and business until his death in Parkersburg.