The SNP was thrown into turmoil on Monday evening after the third high profile resignation within the party in a week.
Ms Cherry, the Edinburgh Western MP who was sacked from her frontbench role in the party’s Westminster group in February, has said “a number of factors” had prevented her from “fulfilling the mandate party members gave to me” as she tweeted the announcement of her resignation from the NEC.
Her decision to stand down from the party’s ruling body comes just days after Mr Chapman resigned as NEC treasurer, citing a lack of support and information that had prevented him from carrying out his fiduciary duties.
His resignation came as Police Scotland is in the process of assessing whether a fraud investigation is required after an allegation to the force that £600,000 of “ring-fenced” money had gone missing from the accounts.
Meanwhile former MSP Marco Biagi, who was hired by the party in January to work on a new case for independence, quit his role last Wednesday, privately saying what should have been the “best job in the world had turned into the worst”.
Ms Cherry, who has clashed with the party leadership over a number of issues, including its plan for how to achieve a second independence referendum, said on Twitter: “I’ve resigned from the NEC of @theSNP.
"A number of factors have prevented me from fulfilling the mandate party members gave me to improve transparency & scrutiny & to uphold the party’s constitution. I won’t be making any further comment at this stage.”
Her statement echoed that of Mr Chapman, who tweeted on Saturday night: “Despite having a resounding mandate from members to introduce more transparency into the party’s finances, I have not received the support or financial information to carry out the fiduciary duties of National Treasurer. Regretfully I have resigned with immediate effect.”
The QC, who was part of the successful legal bid to have Boris Johnson’s prorogation of Parliament overturned at the height of Brexit turmoil, is understood to have been unhappy with how the NEC “conducts itself”.
Ms Cherry was elected to the body by party members in November last year after standing on a platform of “improving party governance, increasing transparency and accountability and improving internal democracy” as well as putting “independence front and centre”.
The election of both her and Mr Chapman, as well as nine others to the ruling body, was seen as a challenge to the authority of party leader Nicola Sturgeon and her husband and party chief executive Peter Murrell.
They had all pledged to push for a new independence campaign, reform SNP complaint handling and give a bigger voice to grassroots members.
At the time Ms Cherry hailed the results as a “clear mandate for change in the SNP” and urged the party leadership to listen.
A party source said that one reason Ms Cherry had stood down was because of failure of the leadership to do that.
“There was a bit of a grassroots rebellion last year which got Joanne and other elected,” the source said.
"People were fed up with the direction of the party on independence, questions were being asked about the financial status of the party, and there was a lot of anger about the party’s stance on reform of the Gender Recognition Act.
"They wanted the party leadership to listen to more voices than just those who seemed to be yes women and men.
"But many of the people they displaced from the NEC, as a result of the election, were later brought back onto the body as representatives of fringe groups, and had voting rights, so the idea of party democracy went out the window. That has angered a lot of people even more.”
Some of those who were elected to NEC positions quit the party at the start of the recent Holyrood election campaign, choosing to join Alex Salmond’s new party Alba.
It had been widely predicted both Mr Chapman and Ms Cherry would jump ship along with now-Alba MPs Kenny MacAskill and Neale Hanvey, but both have remained with the SNP.
In a resignation statement published on Monday, former NEC member Dorothy Jessiman, who joined the Alba Party earlier this year, claimed there were grounds for potential irresponsible financial practices by the SNP.
Ms Jessiman wrote: "Thank you for your answer, which confirms the reports I had received that, faced with a situation in which three distinguished and experienced people in the field of finance felt unable to continue offering their free services to the party without comprising their professional integrity, the committee chose not to rectify the underlying situation and instruct the chief executive to make all required information available without delay.”
She added: “I remain unhappy about the presentation of the ring fenced funds in the accounts. I can no longer convince myself that my continuance as a member of the committee will enable me either to uphold the interests of my members or to accept the risk of finding myself and my husband held personally liable for such a reckless attitude to proper governance. Please accept my resignation.”
A party insider said: “The hostility within the party to those who don’t bow to the leadership is beyond describing. [Home secretary] Priti Patel could take lessons from the way some people on the NEC and in the Westminster group conduct themselves.
"The things now being said about Douglas Chapman, that he’s a malcontent, is ridiculous. He’s incredibly hard working and if he’s stood down then there will be a very good reason for it.”
However, a senior party source said: “Cherry and others made a huge song and dance about getting on the NEC, but now they've got there they’ve realised they cannot just ride roughshod over everyone else and they don’t like it. It’s no surprise they’ve quit.”
Responding to Ms Cherry’s resignation, shadow Scotland secretary Ian Murray said: “Losing one member of your National Executive is careless.
“Losing three members of your finance committee, your treasurer and a member of your National Executive probably indicates a party in crisis.
“The SNP have long been gripped by a kind of centralism and secrecy that would make Lenin blush.
“From the failure to provide basic answers on what an independent Scotland would use as a currency, to the radio silence on what is going on in the party’s bank account – the people of Scotland deserve answers now.”
On Sunday Deputy First Minister John Swinney was asked about Mr Chapman’s resignation and the police investigation into party funds, but said he had no knowledge of any inquiry and did not understand why Mr Chapman had quit.
He added: "In addition to that, the accounts are independently audited by external auditors and submitted to the Electoral Commission for scrutiny. There’s a huge amount of scrutiny of party finances that go on. That happens daily within the SNP and so it should.”
It is understood that Colin Beattie MSP, the party’s former treasurer, has taken over the role once again.
The SNP has been contacted for comment.