The approved demerger of South32 takes BHP from 41 assets to just 19, only 12 of which are operated by the company.
Mackenzie said the company's core assets were quite similar and productivity and cost gains would be accelerated.
"I think it will help us do what we've wanted to do much more quickly," he told media in Perth last night.
"Because of the similarity [of the assets], the overhead that we need to support the business will steadily reduce."
Mackenzie will reveal more details on BHP's plans next week.
"Next week I'll be unveiling the medium-to-long term strategy of the new slim-lined, simple BHP Billiton and where we might be able to take things in terms of costs across a number of our businesses and I think you will find that we will be able to withstand a wide range of prices and still get a very decent return for the business," he said.
The Scotsman added that shareholders had been very supportive of the spin-off and BHP's overall strategy, including in iron ore.
"Obviously people have different views on how they want the market to evolve and our shareholders are often shareholders in some of our competitors, but as far as I'm concerned, they know where we stand and we stand for a rational approach as being a low cost producer and one that believes in free markets that ultimately will serve this company very well due to our position on the cost curve," Mackenzie said.
"But I also think it serves the world well and it looks after our customers, so I'm very happy with our approach and I believe the majority of our shareholders would endorse it."
Last month BHP announced a slowing of its iron ore expansion which would defer expenditure on the Inner Harbour, but Mackenzie said the company would still reach the 290 million tonne per annum mark.
"What we are doing is continuing to work productivity hard and that allows us to get more through the existing infrastructure that we manage, but without some of the investments that we've now postponed at the Inner Harbour, it means we're going to get there probably less expensively, but also at a slower rate," he said.
When asked if rival Rio Tinto should pull back production, Mackenzie refused to comment.
"My issue in all these things is actually preserving and defending the role of free markets and free trade that actually maximises efficiencies in the world and ensures the customers of the businesses that we operate in see the benefit of free markets and secure supply at a sustainable price," he said.
Mackenzie indicated future growth investment would move away from iron ore and coal towards oil and copper and, longer term, potash.
While BHP wasn't ruling out mergers and acquisitions, Mackenzie said it would be hard to find projects that matched the strength of its portfolio.
"The kind of assets that we would want would have to rival the amazing portfolio we already have," he said.
"We're not blind, we're open to any opportunity and we certainly have the capability to do that within our balance sheet, and should an opportunity arise we are prepared to move, but it has a tough competition to beat further investment in our own portfolio.
"We're all ears and all eyes, but it has to be one hell of a deal."
Any acquisitions BHP would consider would be at an asset level, rather than a company takeover.
"We're not really interested in buying back complexity and buying a company with a whole bunch of assets we'd rather not have, so we are trying to find a situation where a prize asset might become available, because of some financial challenge that we're not facing due to the strength of our balance sheet," Mackenzie said.
"They're not going to be falling off the backs of lorries very quickly and that's why I'm pleased that we can grow this business very effectively without needing to acquire anything - and that is plan A."
Shares in BHP dropped 0.3% to $A32.24.
