Lord Lang of Monkton said the SNP “would make a grievance out of a ray of sunshine” and that every other issue was subservient to independence.
His successor as Scottish secretary, Lord Forsyth of Drumlean, also said the SNP “are determined to destroy and break up the United Kingdom”.
Their comments came as peers scrutinised how devolved powers will be treated in the flagship European Union (Withdrawal) Bill.
Lord Lang said of the Scottish government: “They’re working to a different agenda. An agenda with only one item on it, and that item is independence.
“Everything in every area of government in Scotland is subservient to that. Hence the neglect that we see of education, the economy and all the other matters that are their responsibility.
“If they can find a way of turning everything that happens into a source of grievance, they will do so. Grievance is their default position.
“They would make a grievance out of a ray of sunshine, if they thought it would help their cause.”
The objections from the Welsh government to Clause 11 of the Bill were not as strong as those in Scotland, said Lord Lang.
“We’re blinding ourselves to reality if we don’t take account of the fact that the Scottish administration has a completely different agenda from this one,” he added.
Lord Forsyth said: “The difficulty we have here in Scotland is that we have the party in power who are determined to destroy and break up the United Kingdom.
“That is their agenda, and as my friend Lord Lang said, every single issue is turned into a constitutional crisis and is a source of dispute.”
He went on to say he doubted the Scottish government “will want to do anything other than continue this dispute”, as he urged UK ministers to “get on with it” as they had already gone as far as any reasonable person could expect them to go.
“If we have a situation where one devolved legislature is able to have a requirement for consent as opposed to being consulted, then we have one part of the United Kingdom able to use its veto to subvert the wider interests of the United Kingdom, and that was never, ever part of the devolution settlement,” said Lord Forsyth.
Conservative Lord Mackay of Clashfern, a former lord chancellor, has tabled an amendment to the Bill.
It calls for a joint committee from the UK Government and devolved administrations to decide which devolved areas to include in UK-wide frameworks, on the basis they must relate to maintaining the UK single market.
While the amendment proved broadly popular, Lord Forsyth said such a measure would “change and alter our constitution”.
He added: “As I look at the amendment, I think ‘who will speak for England’?
“The Secretary of State’s responsibilities are for the whole of the United Kingdom, not for England.”
Lord Forsyth also said Tony Blair regretted introducing devolution in Scotland given the impact it had on Labour’s footing in the country, a claim rejected by Labour’s Lord McConnell of Glenscorrodale.
Lord McConnell, a former Scottish first minister, urged the Government to be more ambitious about its engagement with the devolved administrations, and suggested rotating the role of chair at joint meetings between different governments.
He also said joint ministerial committees “had never worked”, adding: “Tony Blair and I both tried to get rid of them, frankly. We didn’t succeed, but I wish that we had.”