The BT Sport pundit has jumped to the under-fire Gers coach's defence following his recent dressing-room bust-up with senior players Kenny Miller and Lee Wallace, and the heavy defeat to the Hoops in the semi-finals of the Scottish Cup.
Rangers chairman Dave King has refused to publicly back Murty during a trying time for the Ibrox outfit, and Sutton believes that the Gers boss has been "undermined".
"Would I hang around if I was Graeme Murty? No. Why would he hang around?" The Scotsman quotes Sutton as saying.
"This is a guy who went to Rangers as head development coach to try and further his coaching career, to build and gain experience. He is then launched in at the deep end. What has happened in the last week, you can see it is a toxic place.
"He's not been backed by the hierarchy, then for the players to turn, with the whole suspension thing this week, tells its own story. He has been undermined."
Rangers' hopes of landing silverware all but ended with the defeat to Celtic, with the second-placed Gers lying 13 points behind the table-topping Hoops in the Scottish Premiership.