This is actually a very interesting historical account of the Tenure of Office Act (which was fully repealed way back in 1887).  IOW, President Trump has every right to fire Mueller if that's what he decides to do.

Later in the opinion SCOTUS actually declares the Tenure of Office Act illegal.

Which brings us to the current political situation. There are not one but two bills in the Senate -- both proposed by Republicans -- to make it illegal for Donald J. Trumpto fire Special Counsel Robert Mueller. One bill, sponsored by South Carolina's Foghorn Leghorn senator and Mini-McCain Lindsay Graham, the other by RINO Chamber of Commerce honorary member and pro-high heel-wearing-in-the-military man Thom Tillis of North Carolina. (What is in the water in the Carolinas? Maybe they should get rid of the lead pipes down thar!) Both make it illegal for the President to fire an employee of the Department of Justice without "cause" to be determined by a panel of judges.

This is a clear violation of Separation of Powers. Congress may investigate the matter itself, but they cannot force Mr. Trump to conduct an investigation of himself and force him to retain hostile personnel. And there is no underlying crime being investigated by the President or his staff, but rather a national security issue. The President has an absolute legal right to fire Mueller when he sees fit.

Former Reagan budget director David Stockman thinks Trump is Nixon. He's dead wrong; Trump has the ability to circumvent the gatekeepers in the media and the Washington establishment, something not true of Nixon. Nixon was a true swamp critter, not a maverick outsider (unlike John McCain, whose only claim to “maverick” status is his willingness to stab his friends in the back.) And Trump's policies are poised to reignite the American economy, something that Nixon's supply-side thinking could not do.

http://www.americanthinker.com/articles/2017/08/the_new_tenure_of_office_act.html