Waves of selling battered stock indexes from New York to Shanghai on Monday as fresh trade threats between Beijing and Washington raised fears of an economic slowdown.

The Dow Jones Industrial Average fell 767.27 points, or 2.9%, to 25717.74, notching its biggest one-day percentage drop since December. The S&P 500 shed 3% to 2844.74 and the Nasdaq Composite declined 3.5% to 7726.04. All three major U.S. indexes are now virtually even with where they were a year ago.

Among...