Born in Nice, France, to John L. Mitchell, a wealthy Wisconsin senator, and his wife Harriet Danforth (Becker), Mitchell grew up on an estate in what is now the Milwaukee suburb of West Allis, Wisconsin. Mitchell's father served in the American Civil War as a 1st lieutenant in the 24th Wisconsin Volunteer Infantry Regiment along with future general Arthur MacArthur the father of General Douglas MacArthur. The elder Mitchell served as a United States Senator from 1883 to 1889. His grandfather, Alexander Mitchell, a Scotsman, established what became the Milwaukee Road railroad and the Marine Bank of Wisconsin. Mitchell Park and the shopping precinct of Mitchell Street were named in honor of Alexander. Mitchell's sister Ruth fought with the Chetniks in Yugoslavia during World War II and later wrote a book about her brother, "My Brother Bill".