During his time training with Mishin, Griazev learned the triple Axel jump. Griazev placed 14th at the 2002 Junior Worlds, after which Mishin sent him to work with his wife, Tatiana Mishina. Griazev left Yubileyny, returned to Perm, and did not skate at all for three months. In summer 2002, Griazev moved to Newington, Connecticut to train with Tatiana Tarasova on the suggestion of Alexei Yagudin. He became the 2004 World Junior Champion. That same year, he won bronze at Russian senior nationals and earned a chance to compete at the 2004 European Championships and 2004 World Championships, where he placed 8th and 12th, respectively.