The Labour leader faces a growing rebellion after imposing a three-line whip requiring his MPs to back the Bill allowing Theresa May to trigger Article 50.
Cardiff Central MP Ms Stevens quit becomes the first member of Mr Corbyn’s top team to resign over the issue.
She follows shadow education minister Tulip Siddiq in quitting, while two whips - supposedly responsible for party discipline - have indicated they will also rebel and risk being sacked.
Ms Stevens said: “Theresa May is now leading our country towards a brutal exit with all the damage that will cause to the people and communities we represent.”
She said she had argued against the imposition of a three-line whip and said a “great many” of her constituents had urged her to vote against triggering Article 50.
She told Mr Corbyn: “I accept the referendum result is to leave. I also accept that the parliamentary numbers are such that Article 50 will be triggered and we will leave the EU.
“But I believe that leaving is a terrible mistake and I cannot reconcile my overwhelming view that to endorse the step that will make exit inevitable is wrong.
“I expect this to be the most important vote I will ever cast as an MP and for me it is a clear issue of principle and conscience.”
Mr Corbyn responded to Ms Stevens’s resignation saying: “I understand the difficulties that Jo, and other MPs, have when facing the Article 50 Bill. Those MPs with strong Remain constituencies are understandably torn.
“We have said all along that Labour will not frustrate the triggering of Article 50 and to that end we are asking all MPs to vote for the Bill at its second reading next week.”
In a sign of the revolt facing Mr Corbyn, party whips Jeff Smith and Thangam Debbonaire have said they are prepared to go against his orders.
Shadow transport minister Daniel Zeichner - whose Cambridge constituency voted for Remain in the referendum - said he would defy his party leader because it was a “very straightforward decision” for him to take.
He said the party’s leadership was aware of his intentions: “They know my position and they understand exactly why I’m doing what I’m doing and it’s for them to decide what to do next.”
Bristol West MP Ms Debbonaire said she was prepared to lose her job as a whip to represent her Remain-supporting constituency.