Globally, the COVID-19 pandemic has induced a mental health crisis. Social media data offer a unique opportunity to track the mental health signals of a given population and quantify their negativity towards COVID-19. To date, however, we know little about how negative sentiments differ across countries and how these relate to the shifting policy landscape experienced through the pandemic. Using 2.1 billion individual-level geotagged tweets posted between 1 February 2020 and 31 March 2021, we track, monitor and map the shifts in negativity across 217 countries and unpack its relationship with COVID-19 policies. Findings reveal that there are important geographic, demographic, and socioeconomic disparities of negativity across continents, different levels of a nation's income, population density, and the level of COVID-19 infection. Countries with more stringent policies were associated with lower levels of negativity, a relationship that weakened in later phases of the pandemic. This study provides the first global and multilingual evaluation of the public's real-time mental health signals to COVID-19 at a large spatial and temporal scale. We offer an empirical framework to monitor mental health signals globally, helping international authorizations, including the United Nations and World Health Organization, to design smart country-specific mental health initiatives in response to the ongoing pandemic and future public emergencies.