China's main index lost 2.5% and Tokyo fell 2%. Markets in Hong Kong, Sydney and Seoul also retreated.
Beijing allowed its yuan to fall past the politically sensitive level of seven to the dollar on Monday following Trump's threat last week to extend punitive tariffs to an additional $300 billion of Chinese imports. Also, the Ministry of Commerce announced it was suspending promised purchases of American farm products.
On Tuesday, the yuan fell further to 7.052 to the dollar in early trading. That came after the U.S. Treasury Department officially labeled Beijing a currency manipulator, a status that opens the way to possible additional sanctions.
"Equities are slumping. They will slump more. Bond yields are tumbling. They will tumble far more," said Rabobank in a report.
"Worry about global trade flows, as a stronger USD rumbles through the real economy and U.S.-China divorce smashes supply chains," the bank said.
The Shanghai Composite Index fell to 2,749.85 and Tokyo's Nikkei 225 retreated to 20,299.69. Hong Kong's Hang Seng gave up 2.2% to 25,560.68 and Seoul's Kospi shed 0.5% to 1,937.92.
Sydney's S&P-ASX 200 retreated 2.6% to 6,468.30 and markets in Taiwan, New Zealand and Southeast Asia also declined.
On Wall Street, stocks suffered their biggest loss since December.
Investors already were unnerved about a cooling global economy and falling U.S. corporate profits.
The Standard & Poor's 500 index dropped 3% to 2,844.74. The Dow Jones Industrial Average lost 2.9% to 25,717.74, and the Nasdaq composite fell 3.5% to 7,726.04.
The sell-off began Monday in Asia, where indexes lost more than 1%, and intensified as it swept westward through Europe to the Americas. Investors in search of safety herded into U.S. government bonds, which sent yields plunging.
The yield on the 10-year Treasury note fell to its lowest level since 2016, down to 1.72% from 1.85% late Friday. The yield on the two-year note sank to 1.58% from 1.71%. Both are unusually large moves.
Technology stocks bore the brunt of Monday's selling. Apple slid 5.2%. It not only depends on Chinese factories to assemble its iPhones, but China is also the only country aside from the United States that accounts for more than 10% of its sales.
ENERGY: Benchmark U.S. crude rose 32 cents to $55.01 per barrel in electronic trading on the New York Mercantile Exchange. The contract fell 97 cents on Monday to close at $54.69. Brent crude, used to price international oils, gained 43 cents to $60.24 per barrel in London. It dropped $1.92 the previous session to $59.81.
CURRENCY: The dollar gained to 106.15 yen from Monday's 106.15 yen. The euro strengthened to $1.1229 from $1.1204.