Ms Miller singled out Andrea Jenkyns, mocking the MP for her pledge to “go down fighting” in the ongoing Brexit negotiations.
And the prominent Remain campaigner branded Ms Jenkyns a “Brextremist” in the extraordinary attack.
Writing in the Independent, Ms Miller said: “With Brextremists like Andrea Jenkyns, the MP for Morley and Outwood, now talking about ‘going down fighting’ – as if they were members of some terrorist cell, rather than a group of responsible politicians putting forward any rational proposals – it’s time the great silent and not-so-silent majority made their feelings known about Brexit.
“We must shout with one voice: ‘Not in my name!’”
It follows Ms Jenkyns’ post on Twitter saying that the UK should not give in to the EU.
Ms Jenkyns said: “It is better to go down fighting and honouring the democratic decision of our British people. Then to be long remembered for waving a white flag and surrendering to EU demands. All Brexiteers in Gov and on the backbenches its time to #StandUp4Brexit and finally #ChuckChequers.”
Ms Miller went on to claim that previous generations would not have allowed Brexit.
She said: “I can’t imagine that Brexit – a dogma so obviously against the national interest – would ever have been allowed to get as far as it has by that gutsy, morally robust wartime generation.
“They had learnt, too, through blood and anguish, how important it is that Europe is united.”
Ms Miller’s latest intervention comes ahead of a People’s Vote march in London, calling for another public vote on Brexit.
The Remainer said: “This Saturday, 20 October, I will be proud to join what promises to be the biggest ever march against the madness of Brexit.”
More than 100,000 people attended a People’s Vote march earlier this year in June.
It comes as Theresa May battles to reach a Brexit deal with the EU, with the two sides at a deadlock just months before the UK is due to leave the bloc.
The Prime Minister’s Chequers deal has faced heavy criticism from both Leave and Remain MPs and the EU.
Mrs May today pleaded with her Cabinet to “stand together and stand firm” on Brexit in a meeting at 10 Downing Street.