A member of the Democratic Party, he represented Arkansas as a U.S. senator in 1861.

He graduated from the University of Nashville, in 1833, and from the Jefferson Medical College in 1836; moved to Washington, Arkansas, and practiced medicine for 25 years.

[1] He was a member of the Arkansas House of Representatives in 1848; receiver of public moneys, from 1853 to 1856; unsuccessful candidate for election in 1860 to the 37th United States Congress.

Mitchel was elected as a Democrat to the United States Senate, and served from March 4, 1861, until July 11, 1861, when he was expelled for support of the Confederacy.

He was then elected to the Confederate States Senate at the first session of the Arkansas General Assembly and served until September 20, 1864, when he died the day after his forty-ninth birthday.