In brutal exchanges during a seven-way televised election debate, the Commons leader attacked Ms Rayner for being clueless on the issue.
Labour's deputy leader insisted strains on the public sector are down to government cuts rather that high levels of migration.
But Ms Mordaunt shot back that Labour has "no target, they have no clue," and would allow "uncontrolled immigration".
She told Ms Rayner: "Your leader campaigned for free movement.
"Keir Starmer has spent most of his life campaigning for free movement. These guys are not going to control immigration."
Ms Mordaunt said immigration is too high and the Tories will introduce a cap. She said: "The best way to do this is to get Parliament to have an annual cap. What that will do is take into account the economic needs, the needs of the workforce, but also the pressures immigration puts on communities."
Ms Rayner said Labour would scrap the Rwanda scheme. She added: "We would put that money into a Border Force Command which would be able to smash the gangs because we need to do that.
"And 14 years of the Conservatives, they're relying on overseas to fill our skills shortages because we haven't got an industrial and skills strategy." Reform leader Nigel Farage said the country was facing a population crisis following changes introduced by Sir Tony Blair that have led to record numbers.
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