In an outspoken attack, the Liberal Democrat leader - a committed Christian - said the Prime Minister has shown her "true colours" by "doubling down" on her commitment to cut net migration to the "tens of thousands".
He told the Independent: "By emphasising how immigration must be reduced, she feeds the lie that immigrants are a drain on our country.
"The result of this poisonous propaganda is people being beaten within an inch of their lives in vile hate crimes."
Mr Farron, who will visit Lib Dem-held Leeds North West on Saturday, will also urge Mrs May to drop international students from figures counting towards the net migration target, a stance apparently backed by some Cabinet ministers including Foreign Secretary Boris Johnson and International Trade Secretary Liam Fox.
The Lib Dem leader said that while the PM has committed to leaving the European single market to regain full control over immigration, her own ministers have now acknowledged it cannot be cut because Britain needs foreigners to fill job vacancies.
"So Theresa May could find herself in the ludicrous position of leaving the single market to reduce immigration but with immigration actually staying the same or even going up," he said.
"All she would have achieved is massive social division, and reducing the size of the UK economy by £200 billion over 15 years."
Cutting EU migration would put British people's health at risk as the NHS would collapse without migrant doctors and nurses, while the Government is offering "pathetic" funding to train British workers to fill jobs, he said.
"To me this whole debate is about more than money.
"Britain has been successful in recent years in part by becoming a mecca for some of the most talented, industrious people on earth.
"Not only have they boosted our economy, they have made Britain the most fascinating, liberal society on earth."
Mr Farron's attack on the Tory leader came as he claimed the Lib Dems can replace Labour as Britain's main opposition party because Jeremy Corbyn is "demonstrably the worst leader in British political history".
Despite opinion polls showing the Lib Dems lagging far behind Labour on around 10%, Mr Farron called on voters who want a strong opposition to back his party.
In an interview with the i newspaper, he drew attention to the Labour leader's perceived weakness on security issues, insisting politics needs an opposition "that is proud of its country, that is prepared to defend its country and prepared to defend public services".
He said: "Jeremy Corbyn is a perfectly nice man, but is demonstrably the worst leader in British political history in terms of effectiveness.
"As things stand, a feeble Labour opposition will mean the Conservatives will have untrammelled power.
"Britain needs a decent, strong opposition and my job is to ask the British people to give that job to me."