By Eion Blackwell of AAP
The trust was given ownership of the OK Tedi mine, located in PNG's Western province, by mining giant BHP.
"I will put (Prof Garnaut) on notice that he is no longer welcome to this country," Mr O'Neill told the house during a grievance debate on Friday.
"He can stay out of PNG and conduct himself. I want it out on record in this parliament that we will not tolerate people of such standing coming in and disrespecting leaders of this country."
Earlier, Mr O'Neill referred to a report in The Australian newspaper which quoted Prof Garnaut as saying that with such an accumulation of wealth in PNG, it was "tempting for political figures to think of better ways of using it right now rather than putting it into long-term development".
Mr O'Neill, who was elected in August on a platform of improving the nation's ailing infrastructure, said BHP was running the PNGSDF by remote control from Melbourne and questioned whether PNG had benefited from the project.
"Has it delivered to the expectations of our people, particularly the people of western province?" he said.
"What have they delivered? We have given them a blanket cover, blanket insurance, protection from this parliament that we will never sue them for the damage they have caused to our people.
"We have seen many big announcements about major projects that will change the course of this country over the past 10 years, and yet we have yet to see one of those projects being delivered."
PNG's former prime minister and finance minister Sir Mekere Morauta has been named as chairman of the PNGSDF, replacing Prof Garnaut.