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The Texas billionaire, who owns the NBA's Dallas Mavericks and is a star of ABC's "Shark Tank," tweeted that the proposal creates risk for American businesses.
"Will a trade war with Mexico escalate to the point where US-owned, Mexico-based plants and facilities are at risk?" he posted.
A Twitter user replied to Cuban, asking if he cared more about "American workers or Mexican workers."
"As America goes, so goes the global economy," Cuban replied. "[Trump] cutting off our economic nose to spite our face is bad for every American."
He added that Trump should create a better business environment, such as by slashing corporate taxes as he pledged during the campaign, "and get out of the way."
"America knows how to do business," he wrote.
The 20% tax, loosely referred to as a "border adjustment plan," was floated by White House press secretary Sean Spicer on Thursday only to be walked back slightly as only one of several proposals on the table to help finance Trump's US-Mexico border wall. The tax would be placed on imported goods, but not on exports out of the US. The tax would be paid at the point of purchase.
It was later announced that the tax might be applied to imports from many countries, and not solely Mexico.
Late on Thursday, Cuban, who was a prominent surrogate for Democratic presidential nominee Hillary Clinton during the campaign, claimed Trump would have an approval rating above 60% if he went about his first week differently.
Most polls have Trump's approval rating hovering around 40% to 45%.
"If he took his time on exec orders, didn't talk about himself, crowd size, or voter fraud and let Congress work, his approval would be >60%," Cuban posted.
He followed up, posting that "unfortunately, that's not his DNA."
In Cuban's opinion, "he won't be held accountable," Cuban wrote. "We need to hold everyone that works for him or with him accountable."