Just days before a crunch vote on the issue at the SNP's conference in Perth, the Conservative former Cabinet Secretary compared the stance to believing in the "tooth fairy".
The SNP accused him of ill- informed comments which did not reflect reality.
But in an outspoken attack on the nationalists' plans, Dr Fox told his party's annual conference in Birmingham: "It's also possible to vote to believe in the tooth fairy.
"The idea that you could deal a body blow of confidence to Nato and be welcomed with open arms by Nato is something that is only possible to believe either in Alice in Wonderland – believing two opposite things before lunch time – or in the SNP.
"There is no doubt in any weakening of the Nato position because of the action proposed by the nationalists would not go down well with our allies."
Dr Fox also suggested a new Scottish Defence Force could struggle to replicate the qualities of the British Army, including bravery.
He accused the SNP of failing to recognise that the UK's Armed Forces were more than just the sum of their parts, suggesting that the party saw them as a collection of regiments, ships and planes.
They have "institutionalised excellence, bravery and pride that (don't) come 'as standard' with a piece of equipment", Dr Fox said.
Independence could also mean cutbacks to the duties of the UK's Armed Forces – such as targeting drug trafficking – that would affect Scotland, he warned, continuing: "The drugs can end up in Glasgow as easily as they can end up in London". He also reiterated his previous claims that many Scots would stay in the British Army and not join the new Scottish Defence Force.
The SNP faces a crunch vote at its conference next week as it attempts to overturn its historic opposition to the nuclear alliance.
The party leadership insists that most members of Nato do not have nuclear weapons but a number of the party's MSPs are expected to oppose the plan.
Dr Fox issued a rallying cry, warning: "We must not allow the petty, backward looking and hopelessly ill-prepared nationalists to unravel what so many have selflessly created."
But Angus Robertson, the SNP's defence spokesman, said Dr Fox was in "no position" to lecture Scotland on defence after presiding over base closures cuts and cuts to personnel.
He said: "It's no wonder that people in Scotland do not trust a word the Tories say on defence or any other matter.
"It is only with the powers of a normal independent country that Scotland will be able to end the disproportionate, damaging and dangerous cuts that Westminster continues to preside over."
He continued: "His ill-informed comments do not reflect reality –the vast majority of Nato members do not possess nuclear weapons."