Threat Assessment, Prevention, and Safety Act of 2019 This bill directs the Department of Homeland Security (DHS) to establish a Joint Behavioral Threat Assessment and Management Task Force, which shall provide recommendations to Congress and DHS on the development and implementation of a national strategy for preventing targeted violence through behavioral threat assessment and management. The bill defines behavioral threat assessment and management as the systematic and evidence-based process of (1) identifying individuals whose behavior indicates a capacity for committing acts of violence, (2) investigating and gathering information from multiple sources to assess whether such individuals pose a threat, and (3) the subsequent management of such a threat. DHS shall (1) develop and implement the national strategy and provide information and training services related to it, and (2) award grants to establish community based units for implementing the national strategy.