National De-Escalation of Violence and Community Safety Training Act of 2019 This bill requires the Substance Abuse and Mental Health Services Administration (SAMHSA) of the Department of Health and Human Services to establish a grant program for de-escalation of violence training in communities. Among other requirements, such training must include (1) techniques to de-escalate situations to avoid violence, (2) education about implicit bias, (3) communication and negotiation skills, and (4) scenario-based application of such de-escalation tactics. SAMHSA must establish the De-Escalation Advisory Board to advise and assist SAMHSA's development and implementation of the grant program. Additionally, the bill expands and extends through FY2025 mental health awareness training grants.