Tuton was signed by the Tykes in early 2016 after a prolific spell in non-League with the Shaymen, who he joined in August 2015 from Buxton.
Prior to the Bucks, the 26-year-old had spells with Teversal, Matlock Town and Belper Town.
However, Tuton has struggled to force his way into the first-team at Oakwell.
He has not appeared in a first-team game since April of that year and had loan spells at Grimsby Town and Barrow AFC last season.