"I'm responsible for getting the money together to build the wall, and that's what I'm doing," he said on ABC News' "Good Morning America."
Mulvaney, who unveiled Trump's budget blueprint Wednesday, said the proposed cuts and spending reflect Trump's campaign promises.
"The president wrote a budget for the nation, and we wrote a budget based upon his campaign promises, and that's what you see in the budget," Mulvaney said. "We took his words and turned them into numbers. The president promised a wall. He's going to deliver it."
In the budget blueprint, Trump's promised border wall will get $1.5 billion, with possibly more funds flowing to the project in next year's budget. The money will provide for a couple of "pilot cases" to see what kind of wall structure is most cost efficient and effective, Mulvaney told reporters Wednesday.
"This is a budget blueprint. It's really the spending part of the budget," Mulvaney said. "This is the first piece of the budget to allow the spending process to start in Congress."