This isn't going to happen. He's lying.
To be sure, maybe somebody in the government has been ordered to "consider" this—upon which they left the Oval Office, sat down at their own desk and engaged in a special holiday edition of day-drinking. But the list of countries that "do business" in one form or another with North Korea is extensive, from India to Mexico to Russia to France, and all of those nations are dwarfed in those dealings by China, North Korea's primary international sponsor. The United States isn't going to "stop all trade" with China. It's ridiculous. China isn’t going to "stop all trade" with North Korea regardless, if for no other reason than the unpleasantness of the resulting humanitarian catastrophe just across their own borders.
Either Donald Trump knows this is a pointless and stupid threat or he doesn't. If he doesn't know how ridiculous it is, he is Dumb; if he does, he is just blustering for effect, which only works if you began the day with a bare minimum of credibility to begin with. After a history of similar blurtations, Donald has none. Instead, the whole world rolls their eyes at his pompous, morning television-inspired ad libs.
In fact, Donald Trump's entire "strategy" for countering North Korean nuclear threats appears to be confined to whining at other nations via his smartphone. This is probably for the best, since he is an idiot who can reliably make any situation worse just by poking his stubby little mitts into it, but this is something Donald could have done from the confines of his over-gilded New York apartment. We have generally expected a bit more from our presidents than the social media equivalent of drunk-dialing.
Short version: Good God, this man is a waste of oxygen. If John Kelly can’t figure out how to separate this man from his Twitter account Kelly might as well parachute out of the job right now.