If you remember the special prosecutor for watergate, could only be fired by the head of the justice department, which with Sessions recusal, becomes the deputy AG, or the same guy that hired Mueller. And he just said he wasn't going to fire Mueller.
The president can
No, he can't. He will have to fire Rosenstein and appoint a lackey to do it. Then it is only a matter of how many GOP abandon and turn on regulations specify that a special counsel can be fired only for “misconduct, dereliction of duty, incapacity, conflict of interest, or for other good cause, including violation of departmental policies." The reason must be stated in writing and only the attorney general can actually carry out the firing. Trump, and just how fast they do it.