Individuals interested in having their signature removed from a statewide ballot measure would need to complete a sworn affidavit with the required information per SDCL 2-1-18.1 included and turn that form into our office by United States registered mail or delivered by hand.
Individuals can continue to submit affidavits until the Secretary of State’s office considers the petition filed which wouldn’t be until after random sample has been completed showing enough signatures to place the measure on the ballot.
The Secretary of State’s office holds the withdrawals, and should there be a court challenge, those withdrawals will be available to the parties involved in the court challenge. The office does not keep track of how many have been turned in and simply files any that are submitted.
Please see our page on Challenging a Statewide Ballot Question.
2-1-18.1. Petition  signature withdrawal--Written notification. 
  An  individual who has signed a petition to initiate a constitutional amendment or  measure, or to refer a law, may submit a written notification to the secretary  of state stating that the individual's name be withdrawn from the petition. A  signature may be withdrawn as provided in  2-1-18.2. 
The  written notification must include: 
(1)    The  title of the petition; 
(2)    The  printed name, signature, residence address, and county of registration of the  individual withdrawing the individual's signature from the petition; and 
(3)    A  statement that the individual is withdrawing the individual's signature from the  petition. 
The  individual’s signature on the written statement must be witnessed and notarized  by a notary public commissioned in South Dakota or other officer authorized to  administer oaths pursuant to  18-3-1. For a  written notification to withdraw a signature to be valid under this section, an  individual must submit the written notification to the secretary of state at  any time before the petition from which the individual is submitting a written  notification for withdrawal under this section and 2-1-18.2 is filed  and certified for placement on the next general election ballot under 2-1-17. 
The  written notification may be delivered by hand, or United States registered mail  to the secretary of state. 
2-1-18.2. Petition  signature withdrawal--Challenge required. 
  If a challenge to a validated  petition is filed pursuant to 2-1-17.1 or 2-1-18, the secretary of state  must provide to each party to the proceeding all written notifications,  submitted under 2-1-18.1, that pertain to the  validated petition being challenged. If a signature is withdrawn pursuant to  2-1-18.1, the signature is deemed  withdrawn from the petition and may not be counted as valid in a challenge. 
2-1-17.1. Submission of affidavit challenging petition to secretary  of state--Appeal. 
  Not more than thirty days after a  statewide petition for an initiated amendment to the Constitution, initiated  measure, or referred law has been validated and filed, any interested person  who has researched the signatures contained on the petition may submit a sworn  affidavit to the Office of Secretary of State to challenge the petition. The  sworn affidavit shall include each specific deficiency other than the  following: 
  (1)    Signer does not  live at address listed on the petition; 
  (2)    Circulator does  not live at address listed on the petition; 
  (3)    Circulator  listed a residence address in South Dakota but is not a South Dakota resident; 
  (4)    Circulator did  not witness the signers; 
  (5)    Signatures not  included in the random sample; and 
  (6)    Petition that  was originally rejected. 
  Any challenge by the same person or party  in interest shall be included in one sworn affidavit. 
  The original sworn affidavit shall be  received by the Office of Secretary of State by 5:00 p.m. central time on the  date. If the sworn affidavit challenges any deficiency prohibited under this  section, that deficiency shall be rejected. A challenge to a deficiency is not  a challenge to the petition as a whole. 
  No deficiency may be challenged a second  time with the secretary of state. The secretary of state's decision regarding a  challenge under this section may be appealed to the circuit court of Hughes  County. Any person who does not challenge a petition pursuant to this section,  may bring a challenge pursuant to 2-1-18. 
2-1-18. Court challenge to petition. 
  Nothing in  2-1-15 to 2-1-18, inclusive, prohibits any interested person  who has researched the signatures contained on a validated petition from  challenging in circuit court the validity of any signature, the veracity of the  petition circulator's attestation, or any other information required on a  petition by statute or administrative rule, including any deficiency that is  prohibited from challenge under 2-1-17.1. The results of the process of signature  verification by the Office of the Secretary of State under chapter 2-1 shall be presumed valid as applied to all  signatures for purposes of considering any additional ground for disqualifying  petition signatures, including any ground listed in subdivisions 2-1-17.1(1) to 2-1-17.1(4), inclusive, and cumulating total valid  signatures to determine the results of an appeal under 2-1-17.1. The summons and complaint for a challenge  under this section shall be served on each petition sponsor as a party  defending the validated petition being challenged. Any appearance by the  attorney general at a challenge under this section shall be limited to the  process of signature verification by the Office of the Secretary of State under  chapter 2-1. For purposes of determining whether a  sufficient number of valid signatures has been submitted, the interested person  may elect to proceed with a challenge limited to the sample generated in  accordance with 2-1-16, with the resulting valid sample percentage  applied to the entirety of the petition signatures.