Cotton cleared waivers and was assigned to Triple-A St. Paul on Friday.
Cotton was designated for assignment earlier this week but will stick in the organization after going unclaimed on waivers. The 30-year-old has a 2.83 ERA, 1.11 WHIP and 31:16 K:BB across 35 innings for the Twins this year, so he figures to be in the mix for a promotion when the team needs bullpen depth.