MANCHESTER, N.H.—Republican front-runner Donald Trump said Monday he would slash funding for the Department of Education and Environmental Protection Agency if he is elected president.

In an interview with The Wall Street Journal and New Hampshire’s WMUR at a local diner here, the businessman said he would do “tremendous cutting” of the federal government. Education policy, he said, should be returned to the states, and he said he would end the Common Core education standards, which conservatives view as federal overreach.

“Education should be local and locally managed,” said Mr. Trump, who also attacked the administration’s environmental policies. “The Environmental Protection Agency is the laughingstock of the world.”

Mr. Trump’s focus on domestic budgetary issues is a new plank in his presidential policy proposals. It is also one likely to appeal in New Hampshire, where voters have long rewarded candidates who promise fiscal restraint and to reduce federal government spending.

Mr. Trump also has been under pressure to specify how he would reduce government spending since releasing a tax plan late last year. Independent analysis of that proposal, which would reduce tax rates for some and remove many from the tax rolls completely, concluded it would balloon the federal deficit.