Born near West Union Church, Pennsylvania, Stockdale graduated from Jefferson College (now Washington & Jefferson College), Canonsburg, Pennsylvania, in 1856. He moved to Pike County, Mississippi, in 1857 and taught school. He graduated from the University of Mississippi at Oxford in 1859 where he studied law. He was admitted to the bar in 1859 and practiced in Woodville, Mississippi from 1859 to 1861. During the Civil War, he enlisted in the Confederate States Army as a private in the Sixteenth Mississippi Infantry in 1861, being promoted successively to lieutenant, adjutant, and major of that regiment. At the close of the war Stockdale resumed the practice of law in Summit, Mississippi. He served as delegate to the Democratic National Convention in 1868.
Stockdale was elected as a Democrat to the Fiftieth and to the three succeeding Congresses (March 4, 1887-March 3, 1895), and was unsuccessful as a candidate for renomination. He was appointed Justice of the Mississippi State Supreme Court December 1, 1896. He died in Summit, Mississippi, January 8, 1899. He was interred in Woodlawn Cemetery.