Support And Value Expectant Moms and Babies Act of 2021 or the SAVE Moms and Babies Act of 2021 This bill prohibits the Food and Drug Administration (FDA) from approving any new drug (either as a brand-name drug or a generic) intended to terminate a pregnancy and imposes additional restrictions on such drugs that are already approved. Under the bill, an already-approved drug intended to terminate a pregnancy may be dispensed to a patient only with a prescription. Furthermore, the FDA may not approve any labeling change that would authorize (1) using the drug after 70 days of gestation, or (2) dispensing the drug by any means other than in-person administration by the prescribing health care practitioner. The FDA must also impose additional restrictions on such already-approved drugs, including by (1) requiring the prescribing health care practitioner to receive a special certification, (2) prohibiting the practitioner to also act as the dispensing pharmacist, and (3) requiring the practitioner to have the ability to provide surgical intervention to the patient. The bill also rescinds any investigational use exemption already granted to such a drug if the bill would have prohibited the FDA from granting the exemption. (Currently, the FDA may grant an exemption to certain market approval requirements if a drug is intended solely for use in safety and effectiveness investigations.)