Dismemberment Abortion Ban Act of 2019 This bill establishes a new criminal offense that prohibits a physician from knowingly performing a dismemberment abortion. It provides a definition of the term "dismemberment abortion." A physician who performs a dismemberment abortion is subject to a criminal fine, up to two years in prison, or both, unless the dismemberment abortion was necessary to save the mother's life. A woman or a parent of a minor who undergoes a dismemberment abortion may file a civil action for damages against an individual who violates this bill. The legislation bars the criminal prosecution of a woman who undergoes a dismemberment abortion for conspiracy to violate the provisions of this bill, for being a principal or an accessory after the fact, or for concealing a dismemberment abortion.