Mitchell was born on November 12, 1900, and was raised in Elizabeth, New Jersey. His father, Peter John, died in 1912. His mother was Anna C. Driscoll. Mitchell attended Battin High School and graduated from St. Patrick High School in 1917. His uncle was the character actor Thomas Mitchell. Mitchell married Isabelle Nulton on January 22, 1923. He began his political career in 1932 as the Union County supervisor for the New Jersey Relief Administration. Six years later he was appointed to the New York City division of the Works Progress Administration.
When Brehon B. Somerwell went to Washington, D.C. to lead the Army Construction Program, he made Mitchell head of the labor relations division of the Army Construction Program. In 1942 Mitchell became director of industrial personnel for the War Department, in charge of one million men. After World War II he returned to the private sector; in 1947 he was director for labor relations and operations at Bloomingdale Brothers. In 1948 he was hired by the Army for personnel work in Germany, and was later responsible for a similar task in Korea. He also sat on the personnel advisory board of the first Hoover Commission.
In 1953 Mitchell was appointed Assistant Secretary of the Army in charge of manpower and reserve forces affairs. Several months later he was nominated by President Eisenhower to replace Secretary Martin P. Durkin, who had resigned in protest in September 1953.
On October 9, 1953, Mitchell became the Eighth Secretary of Labor and served in that capacity for the remainder of the Eisenhower Administration. He was an advocate of labor--he fought against employment discrimination, opposed right-to-work laws, and was concerned about the plight of migrant workers. During a top secret selection process in March, 1958, President Eisenhower appointed Secretary Mitchell administrator-designate of the "Emergency Manpower Agency," making him one of the Eisenhower Ten.
Mitchell encouraged management cooperation, supported labor's right to organize, and sought to improve conditions for marginal workers. He established the administrative machinery of the Landrum-Griffin Act and improved DOL organization and morale while reducing overlapping functions. J. Ernest Wilkins Sr. was appointed Assistant Secretary of Labor for International Affairs in 1954, the first African-American to be appointed to the level of Assistant Secretary in American government. Representing Mitchell and the DOL, Wilkins attended Cabinet meetings--also a first for an African-American.
The Welfare and Pensions Plans Disclosures Act was established on August 28, 1958, followed by the Labor-Management Reporting and Disclosure Act on September 14, 1959. Mitchell supported minimum wages for the soft-coal industry and other industries according to the Walsh-Healy Act.
He is a member of the Labor Hall of Fame.
After a bitter primary, Mitchell was elected Republican candidate for Governor of New Jersey with 43.7% of the vote, defeating State Senators Walter H. Jones and Wayne Dumont, Jr.. He lost the general election to Democratic candidate Richard J. Hughes, receiving 1,049,274 votes versus 1,084,194 votes for Hughes.
Mitchell retired from politics and rapidly advanced in the private sector. In 1961 he joined the Crown Zellerbach Corporation as a director and adviser. A year later he also briefly served as Vice President for Industrial and Public Relations, then as Senior Vice President for Corporate Relations until his death.
On October 19, 1964, Mitchell died of a myocardial infarction ("massive heart attack") in his suite at the Hotel Astor in Manhattan, New York. He is interred in St. Gertrude's Cemetery in Colonia, New Jersey.