WASHINGTON — Anthony Scaramucci, President Trump’s new communications director, vowed on Tuesday to purge the White House staff of disloyal aides in an effort to crack down on leaks, as another member of the press staff resigned from a West Wing reeling from an unfolding shake-up.

“I’m going to fire everybody — that’s how,” Mr. Scaramucci told reporters in the White House driveway, when asked how he planned to identify who had been disclosing information to reporters without authorization and ensure that the leaks stopped. He said he had authority directly from Mr. Trump to do so.

“You’re either going to stop leaking, or you’re going to get fired,” he said.

“If I’ve got to get the thing down to me and Sarah Huckabee, then the leaking will stop,” he added, referring to Sarah Huckabee Sanders, the newly named press secretary who stepped in after Sean Spicer resigned last week in protest of Mr. Scaramucci’s hiring.

Michael C. Short, an assistant press secretary who had been close to Mr. Spicer, resigned just hours after Mr. Scaramucci had been quoted in a news report on Tuesday saying he would be fired. The White House confirmed the move in a terse news release, saying that Ms. Sanders had accepted Mr. Short’s resignation and that officials were “grateful for Michael’s service and wish him well in his future endeavors.”