Farmer Carl Grooms has been planning harvests for decades but now he is getting ready to plow under his nearly ripe peppers and beans because there is no market to buy them—and he doesn’t want to watch them rot.

As the coronavirus pandemic disrupts supply chains, American farmers are dumping milk, throwing out eggs and plowing under healthy crops. Produce suppliers are especially vulnerable to surpluses because fruits and vegetables are perishable and can’t be stored.

“We’re...