Due to the potentially significant benefits for society, forecasting spatio-temporal societal events is currently attracting considerable attention from researchers. Beyond merely predicting the occurrence of future events, practitioners are now looking for information about specific subtypes of future events in order to allocate appropriate amounts and types of resources to manage such events and any associated social risks. However, forecasting event subtypes is far more complex than merely extending binary prediction to cover multiple classes, as 1) different locations require different models to handle their characteristic event subtype patterns due to spatial heterogeneity; 2) historically, many locations have only experienced a incomplete set of event subtypes, thus limiting the local model's ability to predict previously “unseen” subtypes; and 3) the subtle discrepancy among different event subtypes requires more discriminative and profound representations of societal events. In order to address all these challenges concurrently, we propose a Spatial Incomplete Multi-task Deep leArning (SIMDA) framework that is capable of effectively forecasting the subtypes of future events. The new framework formulates spatial locations into tasks to handle spatial heterogeneity in event subtypes, and learns a joint deep representation of subtypes across tasks. Furthermore, based on the “first law of geography”, spatially-closed tasks share similar event subtype patterns such that adjacent tasks can share knowledge with each other effectively. Optimizing the proposed model amounts to a new nonconvex and strongly-coupled problem, we propose a new algorithm based on Alternating Direction Method of Multipliers (ADMM) that can decompose the complex problem into subproblems that can be solved efficiently. Extensive experiments on six real-world datasets demonstrate the effectiveness and efficiency of the proposed model.