Yawney played for the Saskatoon J's of the Saskatchewan Junior Hockey League (SJHL), and then the Saskatoon Blades of the Western Hockey League (WHL). Yawney was drafted by the Chicago Blackhawks in the 1984 NHL Entry Draft, third round, 45th overall. After playing with the Canadian national men's hockey team, Yawney played in the NHL for the Blackhawks, Calgary Flames, and St. Louis Blues.