SNP Tommy Sheppard (Edinburgh East) said Mr Mundell had “staked his reputation” on the plans.
He urged the key Tory figure to “step aside”, claiming he was “out of step with opinion in Scotland at every level”.
Speaking during Commons Scotland questions today, Mr Mundell said: “I make no apology for supporting the Prime Minister’s deal.
“I believe that it was the right deal for Scotland and the UK, and of course we will engage constructively with the First Minister and the Scottish Government, but if we are to do so then they must bring forward proposals other than stopping Brexit and starting another independence referendum.”
Mr Sheppard said: “Last night this place made history. We defeated the Government’s plans by an unprecedented majority.
“These are plans on which the Secretary of State has staked his reputation and on which his fingerprints are indelibly printed.
“Given that massive defeat, will he commit now to meaningful engagement with the Scottish Government and consideration of alternative plans, including remaining in the single market and the customs union?”
Mr Sheppard added: “I was going to suggest that the Secretary of State is ill-equipped to take this process forward in Scotland, but he makes the argument for me.
“Given his refusal to engage properly in discussion about alternatives, given the fact he is so out of step with opinion in Scotland at every level, will he now do the decent thing and resign, step aside so that someone else can take this forward?”
Mr Mundell insisted he was “not out of step with opinion in Scotland”, adding: “People in Scotland do not want another independence referendum and they recognise that the SNP has weaponised Brexit in order to try and deliver such a referendum.”
SNP deputy Westminster leader Kirsty Blackman called on Mr Mundell to “encourage” the Prime Minister to extend Article 50.
Mr Mundell replied: “The Prime Minister has set out quite clearly that it is not her intention to request an extension of Article 50.”
While Lib Dem deputy leader Jo Swinson called on Mr Mundell to make a personal commitment that “he will do everything in his power to protect Scotland from the catastrophe of a no-deal exit including putting his country above his party and his own position”.
Mr Mundell said: “I’ve been very clear on the ramifications for Scotland of a no-deal Brexit and why I wanted to avoid that and that’s why I voted for the deal, but I’m also clear on the position that I stood in the 2017 general election on a manifesto of delivering an orderly Brexit for Scotland and the rest of the UK.”
Labour’s shadow Scotland minister Paul Sweeney claimed Theresa May’s Government was responsible for pursing an agenda where “immigrants are demonised” and called on the Secretary of State to apologise.
Mr Mundell replied: “Of course I don’t accept his characterisation of events. Scotland remains a place which should be welcome for migrants wherever they come from.”
SNP Neil Gray (Airdrie and Shotts) said: “The Brexit driven reduction in migration will see real GDP drop 6.2 per cent by 2040, which has a monetary value of about £6.8 billion and a £2 billion cost to the Government revenue.”
While party colleague David Linden (Glasgow East) said: “When will he get out and understand Scotland’s immigration needs are entirely different from this London-centric policy of this British Government.”
Mr Mundell repeatedly argued the policy was out for consultation, adding: “It is a year-long engagement process across the whole of the UK including Scotland.”
Mr Mundell and Speaker John Bercow also praised Andy Murray’s contribution to tennis after reports he is considering his future in the game.
“This has been a momentous week for Andy Murray, so I’m sure you will agree that it’s appropriate at this Scottish questions that we acknowledge in this House Andy’s extraordinary contribution to British sport and his personal resilience and courage,” Mr Mundell said.
Mr Bercow added: “He is the embodiment of guts and character and the most terrific ambassador for Scotland, for tennis and for sport.”