Securing Americas Rare Earths Supply Act of 2019 This bill revises requirements related to the acquisition and disposal of certain rare earth materials, such as those that contain scandium. The Department of Defense must establish guidance for the acquisition of items containing rare earth materials and establish a secure supply chain from appropriate sources. The bill requires the disposal of 3 million pounds of tungsten ores and concentrates stored in the National Defense Stockpile. The bill also authorizes the acquisition of specified materials determined to be strategically and critically required to meet the defense, industrial, and essential civilian needs of the United States. In addition, the bill expands the prohibition on the exchange of sensitive materials with non-allied foreign nations to include additional materials.