Giving a statement in the Commons, Ms Cooper said the figure of £700m included £290m of payments to Rwanda, the cost of chartering flights that never took off, detaining hundreds of people and then releasing them, as well as paying for more than 1,000 civil servants to work on the scheme.
The £700m figure is higher than those previously in the public domain, but includes additional costs such as for detention and civil service salaries.
"A scheme to send four people, it is the most shocking waste of taxpayers' money I have ever seen," she said.
"Looking forward, the costs are set to get worse. Even if the scheme had ever got going it's clear it would only cover a minority of arrivals, yet a substantial portion of future costs were fixed costs."
Ms Cooper added that over six years the government had planned to spend more than £10bn of taxpayers' money on the scheme.
However, Mr Cleverly accused Ms Cooper of "hyperbole" and "made up numbers".
He claimed Labour had scrapped the Rwanda scheme on "ideological grounds", arguing it was needed as a deterrent.
He added: "The level of discourtesy, directed towards the people and government of Rwanda is quite breathtaking.
"To have them read about this decision in the papers before anyone from government had the good grace to formally notify them, I think, is an error, and no one in this House believes for a moment that that level of discourtesy would have happened had this partnership been with the European country."
Mr Cleverly also questioned where people who arrived on small boats from countries like Afghanistan, Iraq or Syria would be sent if they could not be returned home or removed to Rwanda.
