Litigator David Boies and the law firm he founded, Boies, Schiller & Flexner LLP, have stopped doing legal work for Theranos Inc. after disagreeing about the strategy for handling ongoing government investigations of the blood-testing company, according to people familiar with the matter.

Mr. Boies, 75 years old, has been one of the country’s best-known litigators since the late 1990s. He became Theranos’s outside counsel after being approached in 2011 by two investors in the Palo Alto, Calif., startup. He fiercely defended...