The sharp rise appears at odds with a "general decline" among people and firms seeking statutory help with debt, according to the Scottish Government.
But Bryan Jackson, of business advisers BDO, said: "Though the economy is in recovery, many Scottish businesses are still struggling to cope with the triple challenge of rising inflation, staff costs and slow spending.
"Unless troubled businesses see a perceptible upturn from the wider recovery, many will be left fighting to survive. Ironically, it isn't surprising to see more corporate failures as the economy picks up."
The 70% increase reflects the difference between the first three months of this year and last year, according to the figures published by the Accountant in Bankruptcy (AiB).
A far lower increase of 6.6% was recorded between the last three months of 2013 and the start of this year.
Personal insolvencies dropped by 14% to 2,998 when the first three months of each year are compared.
The decrease could be explained by the "most benign interest rate regime ever", according to Mr Jackson.
"With interest rates likely to rise within the next year, many individuals and families will find their mortgage outgoings become impossible to sustain and we may start to see a belated rise in personal insolvencies as a more realistic interest rate regime comes into play," he said.
Overall demand for debt solutions, such as bankruptcy, protected trust deeds (PTDs) and debt arrangement schemes, fell 9.6% between the first two quarters of each year.
Enterprise minister Fergus Ewing said: "Another drop in the number of personal insolvencies is welcome, especially with the figures showing a general decline since 2008-09.
"£8.1 million has been repaid through the Scottish Government debt arrangement scheme this quarter, with a total of £30.0 million repaid in 2013-14, helping to recycle funds into the economy. It is encouraging to see that 10 times more people have chosen to repay their debts under this statutory scheme than the number seven years ago."