The libertarian-leaning Texas congressman said he would wipe out the departments of energy, education, housing and urban development, commerce and interior, along with the Transportation Safety Administration, CBS News reported. He also would cut off war spending.
In a summary, Paul calls his proposals "bold but achievable."
Under a President Paul, the federal workforce would be cut by 10 percent, members of Congress would get paid less and he would draw a salary of $39,336, or "approximately equal to the median personal income of the American worker," his campaign said.
Paul would repeal President Barack Obama's healthcare and financial reforms, and supports cutting the corporate tax rate to 15 percent, extending the George W. Bush-era tax cuts and ending taxes on capital gains and dividends.
Paul said he would keep Medicare and Social Security benefits for older Americans but young workers could opt out.
The New York Times reported Paul envisions his platform would bring the federal budget into balance within three years.
"A lot of people will say, 'Cutting $1 trillion in one year -- that sounds radical," the Times reported Paul told cheering supporters in Las Vegas. "I operate on the assumption that the radicals have been in charge way too long."
Paul made his announcement the day before another Republican presidential debate in Las Vegas.