Stop Shackling and Detaining Pregnant Women Act This bill prohibits the Department of Homeland Security (DHS) from detaining an individual during pregnancy or postpartum recovery and addresses related issues. DHS must immediately release any detainee found to be pregnant, unless the detainee presents an immediate and serious threat of hurting themselves or others. A DHS detention facility may not use a restraint on a detainee who is known to be pregnant, including during labor, transport to a medical facility or birthing center, and delivery, or during postpartum recovery, except for medical or safety purposes. The bill requires DHS to use the least restrictive restraint necessary and prohibits certain specified restraint types, including four-point restraints and binding hands behind the detainee's back. The bill prohibits DHS detention officers from being present during a detainee's pelvic exam, labor, delivery, or treatment relating to a pregnancy, unless specifically requested by medical personnel. If a detention officer is requested by medical personnel, such officer shall be female, if practicable, and remain at a reasonable distance from the detainee. A pregnant detainee must have access to health care services, including comprehensive services relating to reproductive health care and pregnancy. DHS must provide annual training about this bill's requirements to each employee who has a role in the detention or care of a pregnant detainee or a postpartum parent of a newborn. DHS must also provide each detainee notice of their rights under this bill in the detainee's native language.