Cheney, appearing Monday on Fox News, said the proposal is "absolutely dangerous," Politico reported.
"I have not been a strong supporter of Barack Obama. But this really is over the top. It does enormous long-term damage to our military," Cheney said. He said the cuts would be "absolutely devastating."
Cheney said President Barack Obama "would rather spend the money on food stamps than he would on a strong military or support for our troops."
The 2015 Pentagon budget unveiled Monday by U.S. Defense Secretary Chuck Hagel calls for reducing the number of active duty soldiers in the Army to 440,000 from the current size of 520,000, the Defense Department said.
"An Army of this size is larger than required to meet the demands of our defense strategy," Hagel said Monday at a news conference. "It is also larger than we can afford to modernize and keep ready."
The budget proposal would also cut the growth of housing allowances for troops and their families, reduce subsidies provided to military commissaries, and increase healthcare co-pays and deductibles for retirees and active-duty family members.