He was born in Milwaukee in the Wisconsin Territory, the son of Martha (Reed) and Alexander Mitchell, a wealthy banking magnate, politician, and Scottish American immigrant.

[1][2] He graduated from the Hampton, Connecticut, military academy and studied in Europe, spending time in both Munich, Bavaria, and Geneva, Switzerland.

The regiment was quickly thrown into battle, confronting General Braxton Bragg and his Army of Mississippi, which had marched to the vicinity of Louisville as part of the Confederate offensive to seize control of Kentucky.

The 24th Wisconsin was held in reserve for most of the battle, but in the late afternoon was ordered to engage and pursued the enemy as they fled the field.

During this campaign, Lieutenant Mitchell was selected for special service in their brigade, working as a topographical aide to Brigadier General Joshua W.

[3]: 723  It fell to Lieutenant Mitchell to deliver the news to Colonel Nicholas Greusel of the 36th Illinois Infantry Regiment—who was next in line of seniority—that he must assume command of the brigade.

That summer, the Army of the Cumberland was directed to engage Bragg as soon as possible to prevent him from sending additional forces to assist the Confederate defenders at the Siege of Vicksburg.

Lieutenant Mitchell was with the army through the Battle of Hoover's Gap, after which Bragg abandoned Middle Tennessee and moved to defend Chattanooga.

[7] In 1871, he entered politics, running for Wisconsin State Senate on the Democratic Party ticket in the 6th senatorial district (southern Milwaukee County).

After a contentious caucus process, he reached the Wisconsin Democratic Party 4th district convention with strong support and was nominated on the first ballot, defeating Peter J. Somers and John Black.

[9] He won 56% of the vote in the general election, defeating Republican R. C. Spencer, Union Labor candidate Robert C. Schilling, and Prohibitionist Charles E. Reed, and went on to serve in the 52nd United States Congress.

[7] Mitchell married twice, first to Bianca Coggswell and then Harriet Danforth Becker, who was a prominent member of the Daughters of the American Revolution.

His daughter, Ruth Mitchell, was an author and gained some fame as a volunteer fighting the Germans with Yugoslav Chetniks in World War II.

[14] Mitchell was a collector of paintings, including works by Jules Breton, Jehan Georges Vibert, and Adolf Schreyer.

He contributed to the founding of the College of Agriculture at the University of Wisconsin and offered twenty scholarships for poor boys to attend the school.