But for months, Mr. Trump has mocked Ms. DeVos to other aides, making clear that he considers her expendable, according to West Wing officials. When Ms. DeVos was out of office after an injury many weeks ago, White House officials expected that her absence would be used as an opportunity to replace her. That didn’t happen.

But Mr. Trump is not fond of her, White House officials said, and he had no problem making her appear to be the bad actor in relation to the Special Olympics. A White House official denied the characterization.

Others have said that the president does not have a dislike of Ms. DeVos as much as he has apathy toward her and her entire department, and does not generally consider her — or it — worth expending much energy on.