Mitchell, 30, recorded 13 points (6 goals and 7 assists) in 51 regular season games with the Sabres in 2014-15, averaging 15:20 minutes of ice time per game. He produced two game-winners and was assessed 26 penalty minutes.
Baertschi had four assists in 15 games with the Flames this season. He had eight goals and 25 points in 36 games for Adirondack in the American Hockey League.
"In this case, we feel like Sven Baertschi is going to be a top-six [forward], NHL player for our team someday, so we weighed getting Sven versus what we would get in the second round with our pick and we made the decision to go ahead and do it," Canucks general manager Jim Benning. "He's a guy that fits our profile. He is fast, he is skilled. ... We are very happy to have him."