Most people who work at DNI are detailees. They are on loan from other agencies like CIA, NSA, FBI, DIA, DOD, .. 18 agencies. "Firing" them means they just go back to their jobs.

As big part of DNI is to be the principal advisor to the president and as he does not want the advice, cutting DNI's seems reasonable. Director of national intelligence has less things to do when national intelligence has no direction.