Griazev started to skate as a four-year-old in his hometown of Perm when his mother read an announcement that the local skating school was accepting new students. When he was eleven, Griazev moved to St. Petersburg to train with Alexei Mishin. His idol in skating is 1994 Olympic Champion Alexei Urmanov. After a disappointing performance at the 2002 World Junior Championships, Griazev took a break from skating for three months. Then 2002 Olympic Mens Champion Alexei Yagudin suggested that he joins Tatiana Tarasova's group. Coach Elena Buianova (Vodorezova) is the 1983 European silver and World bronze medalist.