Smith played 28 games for the Maple Leafs last season, getting nine points (four goals, five assists) with four penalty minutes.
He also had 10 goals, 16 assists and 10 penalty minutes while serving as captain of the American Hockey League's Toronto Marlies in 2013-14.
Smith made his Maple Leafs debut Oct. 8 against Colorado, becoming the 900th player in franchise history. He missed 24 NHL games because of a broken hand.
The Maple Leafs selected the 19-year-old Valiev in the third round, 68th overall in the 2014 draft.