The CSA will be able to ignore tax returns and certified accounts to make a judgement on standards of living and men may have to explain how they can afford expensive cars, luxury homes and foreign holidays.
"It's the cavalry coming over the hill for a small but important minority of people," Mr Mitchell told The Independent. He referred to evidence highlighted by the CSA of a number of cases where apparently rich men had transferred all or most of their assets into the name of a new wife or mistress.
The measures were foreshadowed in last year's white paper on CSA reform, in response to a storm of criticism of its rigid formula for calculating maintenance payments.
The package, which has now had "flesh put on the bones", will be tested in a pilot scheme in Hastings, East Sussex, in April and should go nationwide at the end of the year.
Men accused of high living while declaring low assets and income will have the right of appeal to an independent tribunal. But groups campaigning against the CSA condemned the new powers as a "snoopers' charter". Paul Doxey of the Network Against the CSA said: "The CSA is giving a great deal of scope to vindictive ex-wives."
Opponents fear that women will be encouraged to spy on their former husbands and collect evidence of high spending. But the Commons social security select committee is expected to publish a report on Thursday backing the plan, which will describe "asset-rich, income-poor" fathers as one of the biggest problems facing lone mothers.
David Shaw, Conservative MP for Dover and a member of the Commons committee, said: "The bottom line is that there are still a lot of men who don't want to pay a penny towards their first family and are becoming increasingly sophisticated at beating the system by passing their money to their companies or to new wives."
In one case, Terri West, a mother of two, campaigned for two years against CSA decisions to reduce her former husband's contributions to zero.
She said she told the CSA that Chris Tsangarides, a record producer, lived in a pounds 300,000 house, had a Porsche, two BMWs and employed a gardener and a cleaner.
The CSA was only allowed to rule on the basis of audited accounts of his company which showed he earned pounds 14,340 a year.
The change to the CSA's remit will be the first time a government agency has been given such powers and is likely to fuel the continuing debate over its activities.