WASHINGTON—The first big tax cut moving through Congress under President Donald Trump would likely benefit the president himself, potentially saving him millions of dollars in taxes on his rental income next year and even more money on other income if he wins a second term.

Mr. Trump’s decision to continue owning his businesses without running them means that he is no longer considered a real-estate professional for tax purposes. That increases the tax’s effect on him and enhances his benefit from the proposed repeal, which...