The former cabinet minister accused Remain supporters of trying to delay the triggering of Article 50 - marking the start of the formal two-year leaving negotiations - in the hope it can be put off indefinitely.
Writing in The Sun On Sunday, Mr Duncan Smith also insisted Britain did not need a deal which allowed it to remain part of the European single market, arguing there was a "strong case" in economic terms for leaving.
His intervention follows reports the Government may wait until the end of next year before invoking Article 50, meaning Brexit may not actually happen until late 2019.
The Prime Minister has said only that she will not make the Article 50 notification before the end of this year, but Mr Duncan Smith said she must get on with it "early" in 2017, rather than wait for forthcoming elections in Germany and France.
"That suggestion is yet another attempt to turn this referendum result into a 'neverendum'," he said.
"For too long membership of the EU sapped our sense of self worth and our self confidence. Now we have the chance to believe in Britain again.
"Let us leave as soon as possible, so that we can get on and make the most of our new found independence."
Mr Duncan Smith warned ministers not to try to negotiate some form of "EU-lite" agreement which would see Britain remain subject to European law, saying that would be to ignore the clear message delivered by the millions of citizens who voted for Leave.
"Tired of handing over billions of their hard earned money to the wasteful EU bureaucrats, it (the referendum result) was an order from the British people to Britain's ruling elite - an order to 'take back control'. That, simply put, means control of our borders, our trade arrangements, our money and our laws," he said.
"What they didn't vote for was EU-lite, or for their Government to engage in negotiations where we bend the knee to Brussels and beg for some concessions whilst remaining in a customs union all the while subject to European law."
He said that Britain did not need to be a member of the single market to trade with it, and may well be better off outside.
"After all in economic terms there is a strong case to leave the single market," he said.
"Being outside returns control over laws and borders and frees the UK from EU regulations, its external tariff and allows us, as a service sector economy, to position ourselves globally, set our trade deals and compete internationally, particularly in financial services."
His comments reflect the deep suspicion among many Leave supporters that opponents of Brexit will try to thwart the referendum result.