Gutierrez, who served under former President George W. Bush, said he worries that the U.S. will push China "over the cliff" and eventually drag down the global economy.
"What I worry about is what if China, instead of growing 6 percent, grows 3 (percent); That we actually have such an impact on the Chinese economy that their growth rate is (stifled) — that will impact everyone and you have to wonder if it's worth it," Gutierrez told CNBC's Oriel Morrison on Thursday.
"That's not good for the world. We may think that China's rise may be bad for the U.S., that China is a strategic competitor ... but the moment China's growth rate declines, we will regret it," he said at the Milken Institute's annual Asia Summit in Singapore.
China is an engine of growth for much of the world. The world's second-largest economy has been the largest contributor to global growth since the global financial crisis in 2008, according to the World Bank.
The extent of China's slowdown depends on "how much damage we do with these tariffs," added Gutierrez, who's now the chair of consultancy Albright Stonebridge Group. He said if the administration of President Donald Trump imposes tariffs on every Chinese product that enters the U.S., the impact on China would be big.
The U.S. has implemented tariffs on $50 billion of Chinese imports — to which Beijing retaliated. Washington has also ended a public comment period for another $200 billion of tariffs worth of goods from China and before that's imposed, Trump said he's "ready to go" with levies on an additional $267 billion worth of Chinese products.
Trump on Twitter: If the U.S. sells a car into China, there is a tax of 25%. If China sells a car into the U.S., there is a tax of 2%. Does anybody think that is FAIR? The days of the U.S. being ripped-off by other nations is OVER!
Trump has frequently taken to airing his criticisms of China in public, including on Twitter. One of his complaints centers on China's trade practices, which he has said hurt American businesses and workers. While some issues that have been raised are worth looking into, calling out China in public can't resolve them, said Gutierrez.
"I would take a private approach. The problem with doing it in public is that it can humiliate a country. We're talking about sovereign countries, not businesses, and to put China in a position of publicly being called out and potentially publicly humiliated, publicly losing face, that can't succeed," he said.
But it's a sign of progress that the U.S. appears to be willing to talk with China, noted Gutierrez, adding that both sides could reach a deal in the end.
"It could resolve in a deal, I just don't know how much it will achieve the president's goals," he said. "We need to understand that trade is part of what drives growth and I think that it's a very dangerous assumption that if our trade deficit is high, we're losing."
The U.S. trade deficit with China was $375.6 billion in 2017, according to data by the Census Bureau. For the first seven months of this year, the U.S. recorded a trade deficit of $222.6 billion with China.