Could Joe Biden countermand Noem's deployment of the National Guard?

The President of the United States and the Dept. of Defense have ultimate authority over the National Guard.  The Governor of the state has full command of the Guard within the state, but must conform to actions approved by the President and Dept. of Defense.

Noem's deployment of South Dakota National Guard personnel to Texas places them under the command of civilian authorities, and in effect removes them from the Department of Defense chain of command in her thinking.  When the National Guard is deployed  in actions outside of their home states, it is usually done at the behest of the President or through designated channels within the Department of Defense.  Some states are responding to the Texas governor's plea for help by sending him state law enforcement officers.  Noem makes clear that she is joining in some retaliatory acts against Joe Biden.  She apparently regards her actions as a transaction between her and the governor of Texas.  A reading of the applicable laws indicate that she is acting beyond her authority.

In particular is the clause that states, "No unit or organization of the South Dakota National Guard and no unit of any branch or arm of the service may be maintained in the state, except as authorized by the President of the United States and recognized by the secretary of defense."(SDCL33-3-3) 

Despite the fact that the deployment is  being paid, at least in part, by a donation, the Guard still operates under federal authority.  The President or someone in the Dept. of Defense chain of command seems to have the basis for courntermanding the deployment and pursuing legal action against it, if they so choose.

Here are the state laws that apply to this instance:

South Dakota Constitution

Article XV§3. Conformity to federal regulations.

The Legislature in providing for the organization of the militia shall conform, as nearly as practicable, to the regulations for the government of the armies of the United States.

State Codified Laws

33-2-6. Circumstances under which militia may be put in actual service.

The Governor may order out from time to time, for actual service, as many of the militia as necessary to execute the laws, preserve order, suppress insurrection, repel invasion, and provide disaster relief assistance.

33-3-3. Composition of military units--Authorization for units by President of United States.

The military units of the National Guard shall be composed and organized, except as otherwise specifically provided, the same as the armed forces of the United States subject in time of peace to such general exceptions as may be authorized by the secretary of defense. No unit or organization of the South Dakota National Guard and no unit of any branch or arm of the service may be maintained in the state, except as authorized by the President of the United States and recognized by the secretary of defense.

33-3-12. Applicability of federal regulations.

The South Dakota National Guard is subject to this title and all orders authorized by this title and rules promulgated pursuant to this title in accordance with the provisions of chapter 1-26. In all matters not specifically covered by this title or by such orders or rules, the National Guard is subject to the applicable regulations of the Department of Defense governing the organized militia and the National Guard, to the Uniform Code of Military Justice, and to the applicable regulations of the armed forces of the United States.

33-3-11. Orders issued by governor--Federal requirements.

The Governor may issue such orders as may be necessary for the government, organization, and discipline of the militia and of the national guard, as provided for in this title or as provided by the rules and regulations for the armed forces of the United States or as issued by the secretary of defense.

33-9-1. Authority of Governor to order active service--Application of other public officials.

In case of war, insurrection, rebellion, riot, invasion, resistance to the execution of the law of this state or of the United States, or in the event of public disaster or upon application of any marshal of the United States, or the mayor of any first or second class municipality or any sheriff in this state, the Governor may order into active service all or any portion of the national guard.

33-1-8. General staff--Composition and responsibilities--Assistants.

The general staff shall include such staff sections as are currently authorized by the Department of Defense in the table of organization for a state headquarters detachment. The responsibilities of the several staff sections and the duties of the several staff officers and administrative assistants shall be such as are prescribed by the regulations, order, or direction, of the Governor or of the adjutant general, and in accordance with the duties of like officers under the regulations of the armed forces of the United States.