2009-10: Valeri Vasiliev skated for Spartak Moscow's 1994-born team in Russia. In 11 games he scored 2 goals with 2 assists and had 16 penalty minutes. Vasiliev played for Spartak's U16 at the Russian Championships – playing in all five games. He had 1 assist and was plus-two with 12 penalty minutes. Spartak lost to Salavat Yulaev in the championship game.
2010-11: Vasiliev played for Spartak in the U18 national championship tournament and led the club's 1994 team in penalty minutes. He saw his first international championship play – representing Russia at a pair of Four Nations tournaments and competing in the 2011 European Youth Olympic Festival. Spartak reached the championship game of the U18 tournament – falling to Vityaz Podolsk. In six games at the tournament Vasiliev scored 2 goals with 1 assist and had 22 penalty minutes. In 24 games for Spartak's 94's he had 89 penalty minutes and scored 3 goals with 9 assists. He played in seven games in the two Four Nations tournaments and was scoreless with 4 penalty minutes. Vasiliev was plus-five with 2 penalty minutes in three games at the EYOF. He was selected by Spartak Moscow in the second round (40th overall) of the 2011 KHL Draft.
2011-12: Vasiliev skated in 18 games for Spartak's junior team MHC Spartak in the MHL and played in three tournaments for Russia. He had 1 goal with 1 assist and was plus-four with 24 penalty minutes in MHL play. He did not play in MHC Spartak's five-game playoff series with Cherepovets. Playing in the U18 Ivan Hlinka and Sergei Zholtok tournaments he was scoreless with 16 penalty minutes in eight games. In four games at the 2011 U19 World Junior A Challenge he had no points with two penalty minutes. Russia finished 2-2 and was fifth in the six-team tournament. Vasiliev was ranked 16th amongst European skaters in Central Scouting's final rankings prior to the 2012 NHL Draft.
2012-13: Vasiliev made his KHL debut as an 18-year-old, skating with Moscow Spartak, and played for the club's U22 team in the MHL. He had 1 assist and was -2 with 4 penalty minutes in 11 games; averaging 12 minutes of ice time in KHL play. Spartak finished seventh in the Tarasov Division. In five Nadezhda Cup games he had 1 goal with 1 assist and was -2 with 2 penalty minutes while averaging 20:38 minutes per game. Vasiliev scored 2 goals with 4 assists and was +5 with 57 penalty minutes in 33 regular season games for Spartak's U22 team and was -1 with 1 assist and 30 penalty minutes in two playoff contests.
Vasiliev is playing for Moscow Spartak in the KHL in Russia for the 2013-14 season.