Cities are crucibles of numerous opportunities, but also hotbeds of inequality. The plight of disadvantaged populations who are ``left behind'' within urban environments has been an increasingly pressing concern, which poses substantial threats to the realization of the UN SDG agenda. However, a comprehensive framework for studying this urban dilemma is currently absent, preventing researchers from developing AI models for social good prediction and intervention. To fill this gap, we construct VulnerabilityMap, a framework to meticulously dissect the challenges faced by urban disadvantaged populations, unraveling their vulnerability to a spectrum of shocks and stresses that are categorized through the prism of Maslow's hierarchy of needs. Specifically, we systematically collect large-scale multi-sourced census and web-based data covering more than 328 million people in the United States regarding demographic features, neighborhood environments, offline mobility behaviors, and online social connections. These features are further related to vulnerability outcomes from short-term shocks such as COVID-19 and long-term physiological, social, and self-actualization stresses. Leveraging our framework, we construct machine learning models that exhibit strong performance in predicting vulnerability outcomes from various disadvantage features, which shows the promising utility of our framework to support targeted AI models. Moreover, we provide model-based explainability analysis to interpret the reasons underlying model predictions, shedding light on intricate social factors that trap certain populations inside vulnerable situations. Our constructed dataset is publicly available at https://github.com/LinChen-65/VulnerabilityMap/.