Clark spoke after President Donald Trump pledged in a speech in Warsaw, Poland, to confront Pyongyang "very strongly."
"There really are no good military options with Korea," Clark said on CNBC's "Squawk Box." "We're at the end of the line at which you can simply fly a couple of B-2 bombers over and threaten North Korea. We've done that in the past. It hasn't worked."
The crisis reached a new peak on the Fourth of July, when North Korea successfully test-fired an intercontinental ballistic missile that experts said could reach Alaska.
Clark believes the White House must answer three questions when approaching the North Korean threat: how the U.S. contains it, how Americans live with it and how can American commitments move forward in that part of the world.
"It's not that you can do a disarming first strike and take out all of its nuclear weapons, take out the missiles, and say, 'OK, there you are,'" Clark said.
A first-strike would lead to immediate retaliation on South Korea and possibly on Japan, according to Clark. He said the U.S. would "end up with a war that causes tens of thousands of deaths."
The four-star general, who led the Clinton administration's military campaign in Bosnia, cited the example of President Dwight Eisenhower in keeping the United States out of war with the Soviet Union. Clark said Trump should follow a similar strategy.
"We've got to think through this and not fall back on the sort of reflex that says we've got the greatest military in the world," he said.
Diplomacy is the answer because "ultimately the Korean people have to resolve this," Clark said. He added that the U.S. must work with China, even though "China's long-term objective is to get us out of Korea and out of the Western Pacific."
Clark said he was pleasantly surprised by Trump's speech in Poland.
In his speech, Trump pledged an unspecified "severe" response and called on allies to take action against North Korea.
"I think that this is a speech which will help the United States reassert its leadership role that it must have in Europe and strengthen the trans-Atlantic bonds," Clark said.