...Of course Trump would really be the one firing Mueller, but he couldn't use the excuse that Rosenstein fired Mueller because of the way Trump botched that excuse bigly in the firing of Comey.
After Watergate, a law was passed allowing the appointment of a Special Prosecutor. The law expired in 1999 and was not renewed. today we have a Special Counsel. It is far easier to remove a Special Counsel vs. a Special Prosecutor.
Special Counsel - The Attorney General may remove a Special Counsel for misconduct, dereliction of duty, incapacity, conflict of interest, or for other good cause, including violation of Departmental policies.
Special Prosecutor - The special prosecutor could only be removed by impeachment and conviction by Congress, or by the Attorney General for "substantial improprieties."
It was a lot harder to get rid of a Special Prosecutor after the "Saturday Night Massacre of Watergate infamy. Today, the A.G. only has to show the vague "good cause" to fire a Special Counsel. To fire a Special Prosecutor, they had to show the higher standard of "substantial improprieties."
If Mueller is fired, The Dems will try to enact the Special Prosecutor law once again. They may be joined by enough Republicans to get it passed with numbers that will overcome a veto. If so, they'll probably appoint Mueller once again.