Minaya cleared waivers Saturday and was outrighted to Triple-A St. Paul, Brandon Warne of Access Twins reports.
Minaya was designated for assignment Tuesday after giving up six runs in 6.1 innings of relief. While he does own a respectable 3.76 career ERA in parts of five major-league seasons, he didn't generate any interest on the waiver wire and will remain as organizational depth for the Twins going forward.