Wittman starred for IndianapolisBen Davis High School from 1975-1978. He averaged more than 23 points a game for Ben Davis, which remains the second highest average at the school, and became one of the nation's top recruits.
The Hoosiers trailed the entire first half of the game until Wittman scored at the halftime buzzer with a deep corner shot. The Hoosers went on to win the game by a 63-50 tally, making the 1981 NCAA tournament the school's fourth national title.
In 1982–1983, with the leadership of Wittman, the No. 1 ranked Hoosiers were favorites to win another national championship. However with an injury to star player Ted Kitchel mid-season, the Hoosiers' prospects were grim. Knight asked for fan support to rally around the team and, despite long odds, the team ultimately won the Big Ten title. Nevertheless in the tournament Kitchel's absence was felt and the team lost to Kentucky in the 1983 Sweet Sixteen. Wittman was named the Big Ten Player of the Year and a consensus second team All-American in 1983. He became a member of Indiana's Hall of Fame and was named to Indiana's Silver Anniversary Basketball Team, in March 1996.
Wittman spent the early portion of his career with the Hawks, sharing backcourt with Glenn "Doc" Rivers and Anthony "Spud" Webb, and starting most of the games from 1985-88 (while averaging 12 points and 3.5 assists in those years combined).
After a small spell with the Sacramento Kings, he became a fringe player with the Indiana Pacers, retiring in 1991-92 after three unassuming years. For his career, Wittman averaged 7.4 points, 1.1 rebounds and 2.2 assists per game, shooting just over 50% from the field.
In 1992, Wittman began his NBA coaching career as an assistant coach, first with the Pacers. He spent one season in Indianapolis and another with the Dallas Mavericks (and later with the Orlando Magic).
On January 23, 2007, Wittman became the head coach of the Timberwolves, succeeding Dwane Casey; he had already started the season as assistant to the former.
On December 8, 2008, club owner Glen Taylor fired Wittman after a 4-19 start, asking Kevin McHale to step in, in a complete change of the organization's structure, as the former Boston Celtics great had been Minnesota's vice-president of basketball operations since 1995.
Wittman became acting head coach of the Washington Wizards, accepting the position after Flip Saunders was fired in January 2012 for a 2-15 start. On June 4, 2012, the Wizards announced that Wittman would be retained as the official head coach of the team for the 2012-2013 season.
His son Ryan Wittman starred for the Cornell Big Red basketball team; he helped lead the Big Red to their first NCAA Tournament appearance in 20 years during the 2007-08 season, again in 2009, and to Cornell's first-ever NCAA basketball tournament victories in 2010 over the Temple Owls and Wisconsin Badgers as the Big Red made its first-ever trip to the NCAA Men's Sweet 16.