WEST MEMPHIS, Ark.—With the help of Medicaid, Stanley Ellis got two hip-replacement surgeries and other care to treat a condition that causes bone tissue to die.

But earlier this year, after an emergency ambulance trip to a hospital here for splitting pain in his shoulder and head, a nurse delivered upsetting news: He had lost his coverage due to a new state work-requirement rule.

“I was hurting so bad, I couldn’t even react,” said Mr. Ellis, a 42-year-old former diesel mechanic who had thought he was exempt from the requirement because he is disabled.

Mr. Ellis is one of more than 18,000 people who were cut from the Medicaid rolls after Arkansas embarked on a closely watched experiment in June 2018, when it became the only state to fully implement a work requirement for program recipients. The outcome in Arkansas could help shape the future of Medicaid, a state-federal program for low-income and disabled people that covers one in seven adults across the U.S. President Trump and Republicans promote the mandate as a way to rein in safety-net costs and increase employment.

In a blow to the GOP, a federal judge in U.S. District Court for the District of Columbia in March blocked Arkansas’ Medicaid work requirement, saying federal officials didn’t adequately consider its potential to cause recipients to lose coverage.