On 11 September 2010, Skavysh netted a last-minute goal against Football Club Naftan Novopolotsk in a Belarusian Premier League game. He also represented the Belarus Olympic team that participated in the 2012 Toulon Tournament and the 2012 Summer Olympics.
Skavysh began his playing career with BATE"s reserve team, and joined the first team during the 2008 season when the club won the league. On 16 October 2010, he repeated the exercise for a 3:2 away win against Dnepr Mogilev. He played in all five of the matches and scored in the 2:0 group stage win against Iceland U21. He made his debut for the senior national side of his country on 3 June 2013, in the 2:0 away win over Estonia in a friendly match.
Skavysh was a member of the Belarus U21 that finished in 3rd place at the 2011 Union of European Football Associations European Under-21 Football Championship.
