Who knows. You won't be watching them on BSN anymore. The Padres had a bunch of different cable options depending on the subscriber. I don't know if those channels play anything at all when there isn't a Padres game.
If your cable provider doesn't get a Twins channel then you'll be able to subscribe through MLB.tv and watch them using a streaming device (Roku, Apple TV, Amazon Fire stick, computer, iPad, etc) assuming you have an internet connection.
I've been Roku/streaming for years now and it's a lot better than cable. For $22 a month I'm getting all the TV I could ever watch. The only thing I miss is Twins baseball.