Mitchell was a graduate of Kingston Collegiate Institute and Queen's University, where he received his Masters of Arts in mathematics in 1894. While at Queen's, he acquired knowledge of the techniques of an astronomical observatory when he was asked to care for the astronomical instruments of the university.

Upon encouragement from his math professor, Nathan Dupuis, he left in 1895 for The Johns Hopkins University to study math under Simon Newcomb, only to find Newcomb retired. Thomas Craig was the new head of mathematics and Mitchell also began study under Charles Lane Poor, the head of astronomy. Poor was an excellent teacher and Mitchell was inclined to follow astronomy from that point on. Mitchell was awarded an astronomy assistantship for his second year at JHU and continued until he received his PhD in 1898 with his thesis published in the Astrophysical Journal, which included a discussion of the amount of astigmatism of a concave grating. While at Hopkins, his astronomy duties consisted of caring for the astronomical transit instrument and the clocks in the little observatory behind the physics laboratory, and the 9.5-inch refractor in the dome of the laboratory roof.

Mitchell set out for the brand new Yerkes Observatory in Wisconsin where he began work as a research student in 1898. Though he enjoyed his work at Yerkes, he was enticed to move away and became an instructor in astronomy at Columbia University in June 1899. Over the fourteen years he was at Columbia, Mitchell taught undergraduate courses in descriptive astronomy both at Columbia and later for girls from Barnard College, a year long course in geodesy for third year students, which continued into a first semester fourth year course, and a six week summer camp for civil engineers.

In 1900, he took what would be for him the first of ten eclipse expeditions. The May 28, 1900 eclipse took him to Griffin, Georgia with the United States Naval Observatory. Mitchell became a world-renowned authority on solar eclipses through his numerous expeditions, including trips to: Sawah Loento, Sumatra in the Dutch West Indies (May 18, 1901), Daroca, Spain (August 30, 1905), Baker, Oregon (June 8, 1918), San Diego, California (September 10, 1923), Van Vleck Observatory, Middleton, Connecticut (January 24, 1925), Fagernas, Norway (June 29, 1927), Niuafoou or "Tin-Can" Island, Tonga, in the South Pacific Ocean (October 22, 1930), Magog, Quebec, Canada (August 31, 1932), and Kanton Island, Kiribati (June 8, 1937), this time as the scientific leader of a National Geographic Society Expedition. An article entitled "Nature's Most Dramatic Spectacle" by Mitchell appeared in the September 1938 edition of National Geographic Magazine. These ten expeditions allowed him to write Eclipses of the Sun, summarizing his work on solar flash spectra, first published in 1923 and produced through five editions (5th edition, 1951). On the 1918 Oregon and the 1925 Connecticut eclipses, Mitchell was accompanied by the artist Howard Russell Butler (1856-1934), whose paintings of totality graced the old Hayden Planetarium of the American Museum of Natural History for many years.

Mitchell went back to Yerkes for the summers of 1909, 1910 and 1911 and then returned for a fifteen month sabbatical in 1912 and 1913. Frank Schlesinger first demonstrated the technique of determining stellar parallaxes photographically at Yerkes in 1905, and Mitchell (along with Frederick Slocum) carried out research applying the technique, publishing their results in 1913. At that point, he was offered the directorship at the Leander McCormick Observatory at the University of Virginia. Mitchell spent much of his time and energy as director coming up with funds for running the observatory and paying staff and graduate students. Mitchell started the use of photographic plates with the visual 26-inch refractor shortly after his arrival at the University of Virginia. He became well known for his work on stellar parallaxes and photometry. Dr. Mitchell was liked by faculty and students alike, known for helping to bring prestige to the University.

Prof. Mitchell was elected an honorary member of the Royal Astronomical Society of Canada on 1958-01-15. JRASC Obit.