Mitchell's parents had immigrated from Lithuania and Paul learned to speak English at school.[2]
He played college football at the University of Minnesota where he was an All-American and had previously attended Edison High School in Minneapolis, Minnesota. At Minnesota he was named to many All-Big Ten and All American teams and was on the Minnesota '41 National Championship Team. He graduated with a Mechanical Engineering degree. He married Minnesota cheerleader and Miss Minnesota Ingrid Vallo, who also worked as a fashion model.[2]
Mitchell was drafted in the 2nd Round of the 1944 NFL Draft (12th overall) but went to serve as a Lieutenant in the Navy during World War II.[3]
After returning he played two full seasons of professional football with the Dons and was traded to the Yanks during the 1948 season. He played with the Yanks for the rest of that season and then three more seasons. In between seasons, he sold Goodyear Tires
After leaving football he worked for the Garrett Corporation (now AlliedSignal/Honeywell) until he retired in 1985 and started his own real estate company in California.