PALM BEACH, Fla.—Mitt Romney, speaking at a private fundraising event on Sunday, offered the first details of deductions he would eliminate or limit in order to offset the income tax cut he has proposed for all taxpayers.

Mr. Romney, the presumptive Republican nominee for president, said he would eliminate or limit for high-earners the mortgage interest deduction for second homes, and likely would do the same for the state income tax deduction and state property tax deduction.

He...