Members have decried the prime minister's move to hold talks with Labour leader Mr Corbyn as the “final straw”.
Pub owner Adam Brooks, from Essex, was one of many to share a photo of his chopped up card.
Mr Brooks said the leader of the Opposition “has no right to be involved” in Brexit talks and Mrs May has “killed” the Conservative Party.
Lawrence Gartshore, 16, said he cancelled his membership hours after the Prime Minister’s announcement from Downing Street on Tuesday evening.
“The Conservative Party are not conservative any longer,” the school student from Warwick said.
“This emphatic capitulation by May was really the final straw.”
Brexit backer Lawrence said he became a paying member about four years ago.
He added the Conservatives could be “redeemed” by a change of leader, and the timing of Mrs May’s talks with Mr Corbyn were the key factor in his decision.
“Please don’t get me wrong, I would have had nothing against her speaking with Corbyn a year ago, earlier on in the Brexit process,” he said.
“But to do so now, so late on, with the clear intention of bullying the party into voting for a customs union – that is deplorable.”
For fellow Brexit advocate Busta Miller, 24, this is the second time he has cut up a Conservative membership card in three weeks.
After his latest card cutting, Mr Miller said: “Asking to meet with Corbyn for a way forward on Brexit was the last straw for me.
“As this incompetent leader has said numerous times, no deal is better than a bad deal. Well that was just another lie among the many and I’m done with it.”
And @Gregorygrace5 tweeted: "Well that's me finished with the Conservative Party. I have cancelled my direct debit and cut up my membership card."
Other Tory party members were in similar unforgiving mood with Mrs May.
@WaltWhi68512022 said on Twitter: "After today, the final straw, Conservative membership card cut up !! So angry !!"
While others branded Mrs May "incompetent", "traitorous" and accused her of a "total lack of respect" for democracy.
On Wednesday, Mrs May was hit by the resignation of Leave-backing Wales minister and whip Nigel Adams, who called the decision to speak with Mr Corbyn a “grave error”.
By contrast prisons minister Rory Stewart welcomed the Prime Minister’s decision, tweeting: “The PM is absolutely right – a no-deal is chaotic and unnecessary – we can do a much better Brexit deal by working together and we must.”
Mr Corbyn welcomed Mrs May’s “willingness to compromise to resolve the Brexit deadlock”, but otherwise avoided the issue during Prime Minister’s Questions.