Teevens also played hockey while at Dartmouth; in Teevens' senior year, the hockey team finished third in the NCAA Men's Ice Hockey Championship. He graduated from Dartmouth in 1979 with an A.B. in history. Teevens was also selected to be a member of the Sphinx Senior Society at Dartmouth.
Teevens' first stint with the Big Green, from 1987 to 1991, showed an upward trend. Beginning with a 2–8 record, Dartmouth then had successive years of 5–5 and 7–2–1. In 1990 and 1991, Dartmouth won the Ivy League championship.
After his first head coaching job at Dartmouth, Teevens was the coach at Tulane University from 1992 to 1996. While he had an overall record of 11–45 in five years at Tulane, he recruited many of the players on the 1998 team that went 11-0.
Teevens coached at Stanford University from 2002 to 2004. In his three years at the Farm, his teams posted a 10–23 record, beat BYU twice and San Jose State three times. However, Stanford failed to improve much during his tenure. Teevens went winless against rivals USC, Cal, and Notre Dame, and never posted a win against a team that finished the season with a winning record. Teevens was fired on November 29, 2004. The Associated Press noted that Teevens was "respected for his class and loyalty" and that he even appeared at the official announcement of his firing.
Teevens was re-hired as Dartmouth's head coach on January 5, 2005, and in the 2005 season, the Big Green posted a 2–8 record. As of the end of 2009, Teevens has an overall record of 35–63–2 as the head coach at Dartmouth. However, in the 2010 season, Dartmouth seemed to turn the corner under Teevens, posting a 6–4 record, its best record in 13 years. In the 2014 season the team was 6-1 in the Ivy League, losing only to Harvard, behind whom it finished in second place.