Suicide is a serious problem in every society. Understanding life events of a potential patient is essential for successful suicide-risk assessment and prevention. In this work, we focus on the Event Detection (ED) task to identify event trigger words of suicide-related events in public posts of discussion forums. In particular, we introduce a new dataset for ED (called SuicideED) that features seven suicidal event types to comprehensively capture suicide actions and ideation, and general risk and protective factors. Our experiments with current state-of-the-art ED systems suggest that there is still room for improvement of ED models in this domain. We will publicly release SuicideED to support future research in this important area.