The South Scotland politician’s comments come after the House of Commons sat on a Saturday for the first time since the Falklands War to debate a second withdrawal agreement.
Mr Smyth said: “The House of Commons has now been presented with two Brexit deals, both of which would destroy local jobs and cut living standards.
“Shamefully our two Conservative MPs plan to vote to put saving their own jobs from Boris Johnson’s axe ahead of saving their constituents jobs and by for voting for both of these deals they are weakening the United Kingdom.”
He added: “It is quite clear that the only way to end this impasse is to have a confirmatory ballot between the proposed deal and remain. It’s time for our local MPs to listen to their constituents and let them make the final decision.”