Some personality traits, especially neuroticism, has been found to be associated with suicide attempt (SA) in mood disorder patients. The present study explored the association between personality traits and SA using polygenic risk scores (PRS) for personality among patients with mood disorders. We also investigated the effects of a variety of psychosocial variables on SA. Patients with bipolar disorder (BPD, N = 841) and major depressive disorder (MDD, N = 710) were recruited from hospitals in Taiwan. Lifetime SA and information on psychosocial factors was collected. We calculated the PRS of neuroticism and extraversion. A trend test for SA was performed across quartiles of the PRS for neuroticism and extraversion, and logistic regression analyses were performed to examine the associations between psychosocial factors and SA, accounting for the PRS of personality traits. The prevalence of SA was higher in MDD than in BPD patients. The risk of SA was elevated in MDD patients with a higher quintile of PRS in neuroticism and a lower quintile of PRS in extraversion. The multiple regression analysis results demonstrated that later age of onset, higher family support and resilience, and lower overall social support were protective factors against SA. From the perspective of suicide prevention efforts, strengthening family support and conducting resilience training for patients with mood disorders may be beneficial interventions in clinical settings.