WASHINGTON—The Trump administration has told employees of the U.S. Office of Financial Research to expect deep budget and staffing cuts, according to people familiar with the matter, the latest example of its efforts to undo policies put in place under former President Barack Obama.

Senior officials at the Treasury Department delivered the news to OFR employees at a Nov. 30 meeting on the 10th floor of the agency’s headquarters in downtown Washington, according to people who attended. It was the strongest indication yet of...