The prospect of losing a vital source of income would force Mexico into a "one-time payment" of $5-10bn (Â£3.5-7bn), says Mr Trump.
But US President Barack Obama said the plan was "half-baked" and unworkable.
Mr Trump made his remarks as voters in Wisconsin go the polls to pick their presidential candidates in each party.
The vote could reshape the Republican race, with front-runner Mr Trump, who has never held elected office, facing a strong challenge from Texas Senator Ted Cruz.
In a memo to the Washington Post, the businessman says he would threaten to change a law to cut off cash transfers.
Building a border wall with Mexico has been a core message of Mr Trump's campaign since day one, when he said there were rapists, drug addicts and criminals coming across the border.
If Donald Trump isn't the 2016 Republican presidential nominee - if some time between now and the end of the party convention in late July the prize slips from his grasp, Wisconsin could be where it all started to go awry.
At this point it's conventional wisdom that Mr Trump has had a terrible week on the campaign trail.
His top aide was indicted for accosting a reporter. He stumbled when trying to answer questions about abortion, angering both the left and the right. Wisconsin's popular Republican Governor Scott Walker endorsed his opponent, Ted Cruz. And Mr Trump saw his lead in this pivotal mid-western state evaporate.
By Sunday evening, at a rally in a half-full downtown Milwaukee theatre, the front-runner was showing signs of frustration. He mocked his opponents in the #neverTrump movement, which has vowed to fight the New Yorker to the July Republican convention and beyond.
Is it all going wrong for Trump in Wisconsin?
The wall plan has been widely condemned by, among others, Pope Francis. Mr Trump has also pledged to deport all 11 million undocumented migrants.
The Mexican central bank said that money sent home from overseas hit nearly $24.8bn last year, more than its oil revenues.
In dismissing the plan, Mr Obama said it would cause the Mexican economy to collapse, sending even more migrants north to find work in the US.
"This is another example of something that's not thought through and put forward for political consumption," he said.
The law Mr Trump wishes to change, as outlined in his memo, is part of the US Patriot Act - he would stop anyone living illegally in the US from sending money overseas.
Just the threat of enacting this would make Mexico "immediately protest," the Trump memo reads, and they would be compelled to pay for the wall.
He also proposed raising visa fees and cancelling visas for Mexicans.
If Mr Cruz wins in Wisconsin, as polls suggest, it will help him close the gap on Mr Trump in the all-important delegate count.
Delegates represent their states at the party's convention in July and are accumulated by the votes in each state.
A Wisconsin defeat would make it is far less likely that Mr Trump will have the 1,237 delegates needed to secure the nomination.
If he falls short, his unpopularity with sections of his party means he could be deprived of the nomination at the summer convention.
Currently, Mr Trump has 735 delegates, Mr Cruz 461 and Ohio Governor John Kasich 143.
Democratic voters are also voting in Wisconsin, with Hillary Clinton facing a strong challenge from Vermont Senator Bernie Sanders after his string of wins.
Republican White House hopeful Donald Trump has said he would stop cash sent home by Mexicans based in the US, until the country pays for a border wall.