Born in Pembroke, Teevens attended Silver Lake Regional High School in Kingston, Massachusetts and Deerfield Academy. He attended college at Dartmouth, and played quarterback there from 1975 to 1978. He was the quarterback of the Big Green team that won the Ivy League football title in 1978. He was an honorable mention All-America that same year. He 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.