Stopping the Abuse, Victimization, and Exploitation of Girls Act or the SAVE Girls Act This bill authorizes the Department of Justice and the Department of Health and Human Services to provide grants to certain governmental and nongovernmental organizations to combat the smuggling and trafficking of children and young women. The focus of this grant program is (1) preventing the smuggling of children and women between the ages of 12 and 24 across the U.S. border; and (2) providing support to such individuals if they have already been smuggled into the United States or if they have been or are at risk of becoming victims of a severe form of trafficking in persons, including child sex trafficking.