A reliable and searchable knowledge database of adverse drug reactions (ADRs) is highly important and valuable for improving patient safety at the point of care. In this paper, we proposed a neural multi-task learning system, NeuroADR, to extract ADRs as well as relevant modifiers from free-text drug labels. Specifically, the NeuroADR system exploited a hierarchical multi-task learning (HMTL) framework to perform named entity recognition (NER) and relation extraction (RE) jointly, where interactions among the learned deep encoder representations from different subtasks are explored. Different from the conventional HMTL approach, NeuroADR adopted a novel task decomposition strategy to generate auxiliary subtasks for more inter-task interactions and integrated a new label encoding schema for better handling discontinuous entities. Experimental results demonstrate the effectiveness of the proposed system.