Khan's power of policing is very limited. He can set objectives, which he has done. But he doesn't control operational matters, and he can't sack the commmissioner, who isn't responsible to the mayor. I can't see any reason to dismiss him for not doing things he has no power to do in the first place. (But then I imagine the real reason people want him sacked is because he's Labour.)
As far as I know, the commissioner reports to Rudd.