Steve was born and raised on the Blackfeet Reservation in Browning, Montana. Son of Curley and Lila Reevis, he is the 4th of 6 siblings. He graduated from Flandreau High School and attended Haskell Indian Junior College in Lawrence, Kansas where he received a degree in arts. After junior college, he left the reservation in Montana to try to begin an acting career in Los Angeles. He lived on the beach in his car, a 1971 Ford Torino, for many months before he began to have a more steady income. He and his wife Macile, an artist and clothing designer, have three children.

In 1996 Steve received an award from First Americans in the Arts (FAITA) for his supporting roles in both the critically acclaimed movie Fargo and in the made for television movie Crazy Horse. In 2004 he repeated this honor for his work on the ABC series Line of Fire.