The powerful combination of large-scale drug-related interaction networks and deep learning provides new opportunities for accelerating the process of drug discovery. However, chemical structures that play an important role in drug properties and high-order relations that involve a greater number of nodes are not tackled in current biomedical networks. In this study, we present a general hypergraph learning framework, which introduces Drug-Substructures relationship into Molecular interaction Networks to construct the micro-to-macro drug centric heterogeneous network (DSMN), and develop a multi-branches HyperGraph learning model, called HGDrug, for Drug multi-task predictions. HGDrug achieves highly accurate and robust predictions on 4 benchmark tasks (drug-drug, drug-target, drug-disease, and drug-side-effect interactions), outperforming 8 state-of-the-art task specific models and 6 general-purpose conventional models. Experiments analysis verifies the effectiveness and rationality of the HGDrug model architecture as well as the multi-branches setup, and demonstrates that HGDrug is able to capture the relations between drugs associated with the same functional groups. In addition, our proposed drug-substructure interaction networks can help improve the performance of existing network models for drug-related prediction tasks.