In an October 1953 game against Duke at the Polo Grounds in New York City, Mischak made an improbable play to seal a 14–13 Army victory that was chronicled in David Maraniss' biography of Vince Lombardi, When Pride Still Mattered. Late in the fourth quarter, Duke running back Red Smith ran a double reverse for what would have been a go-ahead touchdown, but was pursued by Mischak from several yards behind. As Smith neared the endzone, Mischak caught up to him and made a touchdown-saving tackle short of the goal line. Two subsequent stops by the Army defense yielded a historic victory for head coach Red Blaik.
After his playing career, he served as a coach of tight ends for the Oakland Raiders from 1973 and 1987. He died on June 26, 2014 at the age of 81.