Mitchel was born in Union County, Kentucky, but grew up in Lebanon, Ohio. He was educated in Lebanon, Ohio and afterward at West Point in 1825, where he was a classmate to Robert E. Lee and Joseph E. Johnston. He graduated in 1829, placing 15th out of 46 graduates. Mitchel stayed at West Point as assistant professor of mathematics for three years. After holding several military positions while studying law, he went to Cincinnati, passed the bar and became an attorney. He also filled the office of Chief Engineer of the Little Miami Railroad, then in process of construction. Subsequently, in 1836, he became Assistant Professor of mathematics, philosophy, and professor of astronomy at Cincinnati College, and during this incumbency achieved a national renown as an astronomical lecturer and builder of a great observatory (Cincinnati Observatory). He was instrumental in establishing the college's law school, and on his first vacation, surveyed and recommended the route of the planned Little Miami Railroad between Cincinnati and Springfield, Ohio.