S.D. Codified Laws § 21-47-2
If the defendant be a nonresident of the state, or absent or concealed or if he be a resident of the state and after due diligence cannot be found in the state, service may be made by publication in the manner prescribed by statute or rule of court in ordinary civil actions but no additional lien on or seizure of property other than that contained in the mortgage or resulting from commencing foreclosure thereof shall be necessary to obtain jurisdiction of the persons served with process by publication. If the mortgagor or any other proper party defendant is deceased, service upon unknown heirs, devisees, legatees, personal representatives, creditors, and other unknown persons, who might have a right of redemption from the mortgage, may be made by publication, as provided by § 15-9-9.
SDCL 21-47-2