S.D. Codified Laws § 9-8-7
At the first regular meeting after the annual election in each year and after the qualification of the newly elected aldermen, the council shall elect from among its members a president and vice president, who shall hold their respective offices for the municipal year.
The president of the council in the absence of the mayor acts as the presiding officer of the council. During the absence of the mayor from the municipality or the mayor's temporary disability, the president of the council is acting mayor and has all the powers of the mayor.
In the absence or disability of the mayor and president of the council, the vice president of the council shall perform the duties of the mayor and president of the council.
However, the president of the council or vice president of the council acting as the mayor shall only vote as an alderman. No alderman acting as mayor may vote as the mayor to break a tie vote.
SDCL 9-8-7