According to Alexander Warrack's The Scots Dialect Dictionary, the definition he gives for deil’s beef-tub (n) is a roaring linn.
I put it to you that the Devil’s Beef Tub is a roaring linn. It is a place where a devil may take his bath. Moffat the local spa town with its sulphurous spring would reinforce this demonic theme. It is nothing to do with reivers or beef. It is a corruption of bath tub.
“Town in a lather over…..” “Rubba, dub, dub in the Devil’s Beef Tub”?