[2] At the age of 11, he moved from Perm to Saint Petersburg to train with coach Alexei Mishin.

[2] In summer 2002, Griazev moved to Newington, Connecticut, to train with Tatiana Tarasova on the suggestion of Alexei Yagudin.

At the 2006 Russian nationals, Griazev finished 9th and did not receive a berth to the European Championships and the Olympics.

Griazev returned to Russia in March 2006 to take part in the Italian Carnival skating tour produced by Ilia Averbukh.

His touring schedule was cut short when he sustained a knee injury and had to undergo surgery.

He spent spring 2007 performing with Averbukh's skating tour, which traveled to over twenty cities in Russia, as well as shows in Lithuania, Latvia, and Israel.

[7] For the 2007–08 season, Griazev was initially assigned to the 2007 Nebelhorn Trophy competition in Oberdstorf, Germany, but injured ligaments in his ankle in September 2007 and had to withdraw from the event.