This is a timely question, although the practice of appointing a special counsel to investigate allegations against government officials (particularly the executive branch) is not new. In this process, the Attorney General of the United States authorizes the special counsel to investigate a given set of allegations, as well as federal crimes committed with the intent to interfere with the investigation (this includes perjury, obstruction of justice, destruction of evidence, and intimidation of witnesses). The special counsel also has authority to investigate any new allegations that arise and are directly related to the existing investigation. Under regulations in 28 C.F.R. 600.1, there is a three-step analysis in the decision to appoint a special counsel:
1. The attorney general must determine is a criminal investigation of a person or matter is warranted.
2. If a criminal investigation is warranted, the attorney general must determine if a conflict of interest would arise if the U.S. Attorney's Office or Department of Justice litigated the matter.
3. If it would be in public interest to appoint a special counsel.
Following appointment, the special counsel has the authority to investigate with the full power and independence of any U.S. attorney. However, they must consult with the attorney general should new allegations rise directly related to the matter under investigation.
Under section 600.7, removal of the special counsel requires "direct action" from only the attorney general and "only for good cause", i.e. “misconduct, dereliction of duty, incapacity, conflict of interest, or for other good cause, including violation of [DOJ] policies". Therefore, a member of the executive branch (such as the President) does not have the power to directly remove an acting special counsel. The only way for a president to remove an appointed special counsel would be to instruct the attorney general to fire the counsel. Under law, the attorney general could only do so under strict guidelines, and would have to show prove misconduct or incapacity in respect to the special counsel. If the attorney general refused to do this, the President could theoretically replace the attorney general with someone who could carry out the orders to fire the special counsel. However, the political ramifications of this are disastrous; as seen in the 1973 "Saturday Night Massacre" of the Watergate Scandal during which President Nixon replaced the Attorney General Elliot Richardson after he refused to fire special counsel Archibald Cox. Richardson was replaced with Deputy Attorney General William Ruckelshaus, which lead to immense political fallout. Therefore, it is absolutely unlikely that a President have a special counsel removed without significant political, and perhaps criminal, repercussions.