Warren Buffett responded to Donald Trump’s claim that the Berkshire Hathaway Inc. chief had taken a “massive” deduction by offering up details of his 2015 return in a disclosure that hinted at other ways that billionaires can avoid paying much tax.

Mr. Buffett said Monday that he earned adjusted gross income of $11.6 million in 2015 and paid $1.8 million in federal income tax. He said his income was offset by $5.5 million in deductions, which included $3.5 million in charitable donations and almost all of the rest in state...