HM Revenue and Customs and contractor Concentrix were criticised by the Work and Pensions Committee for decision-making "stacked against claimants".
The committee found that 90% of moves to remove benefits were overturned on first appeal.
HMRC said tax credit error and fraud checks would remain in-house in future.
The committee condemned HMRC and Concentrix for "gross failure of customer service".
It said vulnerable people were left in humiliating hardship while Concentrix and HMRC targeted "strike rates" of benefits being removed.
In many cases people lost benefits for months and were forced to borrow money and use food banks to survive, said the MPs.
Committee chairman Frank Field said:  "The committee was horrified to learn of the 'cut first, think later' approach that was deployed by Concentrix.
"Our horror was compounded by the company's - and HMRC's - apparent celebration of its 'strike rate' in cutting families' tax credits.
"The damage caused to families' living standards by this 'strike rate' is still being felt by my constituents needing to rely on food banks while their claims are reinstated.
"Although the committee welcomes HMRC's decision to bring in-house its tax credit compliance functions, we are clear that this will not automatically deliver a better service.
"Nor are those families driven into debt going to be rescued from the plight into which this sorry episode plunged them."
HMRC contracted Concentrix in May 2014 to check for possible fraud and error in tax credit claims. The contract was terminated in November 2016.
The committee said HMRC was negotiating a new contract with Concentrix as late as 8 September.
As a single parent of two young boys, tax credits of more than Â£100 a week were vital to the household budget of Paul Eite.
But in August this year Paul, 39, of Hayling Island, Hampshire, was left desperate when the payments were stopped for seven weeks by HM Revenue and Customs' contractor Concentrix.
After Â£50 worth of phone calls lasting 11 hours, Paul's tax credits were reinstated on appeal.
During those seven weeks, says Paul, stress levels "went through the roof".
"It really does affect you. You're constantly saying 'when's the next money coming in'. It was shocking," he recalls.
"You're panicking about your financial situation. You scrimp and save - you learn how to make a really good meal with beans and toast."
An HMRC spokesman said: "We apologise to all those who were let down by our contractor.
"We took swift and decisive action to end the contract early and took back all outstanding cases which are all now resolved.
"We have made it clear that tax credit error and fraud checks, which play a key role in making sure that people get what they are entitled to, will in future remain in-house."
A Concentrix spokesman said: "We welcomed the opportunity to engage with the Work and Pensions Select Committee it its inquiry.
"This was a hugely complex contract and programme, and as the committee has highlighted, a number of challenges and issues emerged at the outset.
"We welcome any further investigations into the contract, including the National Audit Office investigation, to ensure all lessons can be learned."
A "cut first, think later" attitude plunged tax credit claimants into humiliating hardship and debt, a group of MPs has said.