John Finnie – who will step aside as a parliamentary liaison officer to Mr MacAskill – and Jean Urquhart will sit as independents after Friday's vote at the party's conference in Perth.
The pair went ahead with their decision to quit despite pressure from First Minister Alex Salmond and his deputy Nicola Sturgeon to reconsider.
Mr Finnie's resignation is viewed at Holyrood as a blow to the party, as his experience as a police officer had countered Labour's Graeme Pearson – a former head of the Scottish Crime and Drug Enforcement Agency – on the Justice Committee.
Mr Salmond said he was saddened by the news and added both had been excellent servants to the SNP.
Ms Urquhart, 63, and Mr Finnie, 55, called their decision heart-wrenching. Both stressed they would be supporting the SNP's programme of government and playing their part it in the vote yes campaign in the run up to the independence referendum in 2014.
"Our cause is still independence," Ms Urquhart said.
They were elected as list members for the Highlands and Islands at the election last year. Both had been parliamentary candidates before and had been prominent SNP councillors on Highland Council.
In announcing their decision yesterday in Inverness, they said that although they owe their election to being on the party list and not as a result of a constituency vote, they did not think they should quit as MSPs.
Mr Finnie, who first joined the SNP when he was 16, said: "The views I was expressing during the election were those of the party, which produced a majority government. I haven't changed my position on disarmament and Nato. We fought that election on a policy of withdrawal from Nato and it was a policy overwhelmingly endorsed by the people of Scotland."
The party's long-standing commitment to withdraw from Nato was overturned by 426 votes to 332. Now Nato membership is dependent on the removal of the Trident nuclear weapons, based at Faslane naval base on the Clyde, and on Scotland no longer being asked to host nuclear hardware
Mr Finnie and Ms Urquhart said they accepted the party's commitment to removal of nuclear weapons from Scotland, but couldn't square that with being a member of a first strike nuclear alliance.
Mr Finnie said: "I had very courteous exchanges with the First Minister and his deputy, and have the highest regard for them. I find it hard to envisage circumstances whereby they wouldn't still have my support."
Ms Urquhart, who has been a supporter of independence for 25 years and a CND member for 35 years, added: "The issue of nuclear disarmament and removing Trident from Scotland's waters is a red line issue for me and I could not remain committed to a party that has committed itself to retaining membership of Nato."
Other Nato rebels within the Holyrood group expressed regret at their stance and said they would not be following them.
Fellow Highlands MSP Rob Gibson, himself a Nato rebel, said he was surprised and disappointed to hear about the resignations.
But the other MSPs who backed the original party stance on Nato, mainly Glasgow members, made clear they felt he debate and the vote had ended the issues for now.
Mr Salmond said: "Jean and John have indicated they will continue to support the Government from the back benches, and I welcome that. I also look forward to working with them both in the campaign to achieve a yes vote in the referendum."
Isobel Lindsay, of Scottish CND, said: "Scottish CND have great respect for John Finnie and Jean Urquhart's integrity."
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