S.D. Codified Laws § 11-3-16
Any plat of any municipality or improvement district, or addition thereto, or any subdivision of land therein, may be vacated by the proprietor at any time before the sale of any lots therein, by a written instrument declaring the plat to be vacated, duly executed, acknowledged, or proved, and recorded in the office with the plat to be vacated. The executing and recording of such writing shall operate to destroy the force and effect of the recording of the plat so vacated, and to divest all public rights in the streets, alleys, commons, and public grounds laid out as described in such plat. The register of deeds shall notify the affected municipality or improvement district of the vacation within ten days of filing for a vacation of a plat.
If any lots have been sold, the plat may be vacated by all the owners of lots in such plat joining in the execution of the writing aforesaid.
SDCL 11-3-16