Slepyshev was selected first overall in the 2011 KHL Junior Draft by Metallurg Novokuznetsk. Midway through the 2012–13 season, his second in the Kontinental Hockey League, he moved from Metallurg to Salavat Yulaev Ufa. After the Oilers selected him in the third round (88th overall) of the 2013 NHL Entry Draft, Slepyshev remained in Russia to continue his development with Salavat.