"Can he fire muehler" is a silly question. He can. The question we need him think about is "at what cost?".
The constitution gives the president broad powers over how he manages the executive branch. There is no congressional law (the gop let the independent prosecutor law expire) in place to stop him.
The "office" of the special council isn't even established by law. It is a ruling established by a former USAG and set as policy in the agency. Any AG can undo that rule and abolish the office completely. They don't need to fire muehler, the office and all of its authority would be gone, and muehler and his entire staff would be without standing; many wouldn't even be gov't employees since they were brought in as contractors.
Now muehler would surely start a court battle to keep operating, but that isn't a sure thing. It might take a couple of months for the courts to hear the case, and it would end up at scotus. But he could keep working while that goes on. But eventually, there will be a ruling, and I don't trust this scotus one little bit.
So yes, the orange douchebag can get rid of muehler and essentially bury all work product. The FBI could just notify the courts it is dropping all charges and that would be that.
Except that the constitution does have a remedy. Impeachment. But, that will require 19 republican senators to vote to convict, and those votes don't exist.
So what a ride that would be. But in the end, either trump would be gone or our democracy will be. Once he realizes he won't be impeached, no matter what the charges are, he will move on eliminating media opposition, and really anything that criticizes him or doesn't kiss his arse.
None of the options are particularly encouraging when we are dealing with someone who needs 2 hands to drink out of a sippy cup and who talks with putin more frequently than he talks with the gop leadership..