Suicide is the 10th leading cause of death in the U.S (1999-2019). However, predicting when someone will attempt suicide has been nearly impossible. In the modern world, many individuals suffering from mental illness seek emotional support and advice on well-known and easily-accessible social media platforms such as Reddit. While prior artificial intelligence research has demonstrated the ability to extract valuable information from social media on suicidal thoughts and behaviors, these efforts have not considered both severity and temporality of risk. The insights made possible by access to such data have enormous clinical potential - most dramatically envisioned as a trigger to employ timely and targeted interventions (i.e., voluntary and involuntary psychiatric hospitalization) to save lives. In this work, we address this knowledge gap by developing deep learning algorithms to assess suicide risk in terms of severity and temporality from Reddit data based on the Columbia Suicide Severity Rating Scale (C-SSRS). In particular, we employ two deep learning approaches: time-variant and time-invariant modeling, for user-level suicide risk assessment, and evaluate their performance against a clinician-adjudicated gold standard Reddit corpus annotated based on the C-SSRS. Our results suggest that the time-variant approach outperforms the time-invariant method in the assessment of suicide-related ideations and supportive behaviors (AUC:0.78), while the time-invariant model performed better in predicting suicide-related behaviors and suicide attempt (AUC:0.64). The proposed approach can be integrated with clinical diagnostic interviews for improving suicide risk assessments.