Objective: This study aimed to explore the associations between smartphone overdependence (smartphone addiction) and suicidal ideation and attempts among Korean adolescents to acknowledge the risk of smartphone overuse. Methods: Data were obtained from the results of the 2020 Korea Youth Risk Behavior Web-based Survey. Smartphone addiction was categorized into three groups: adolescents who scored less than 23 were categorized as the general user group and formed the reference, those with scores of 23–30 were categorized as the potential-risk user group, and those with scores higher than 31 were categorized under the high-risk user group. Suicidal ideation and suicide attempt were identified as dependent variables in the present study. Multiple logistic regression was used to analyze the relationship between SA and suicidal ideation and suicide attempt status among Korean adolescents. Results: This study included 41,173 general users of smartphones, 12,142 potential-risk users, and 1633 high-risk users from among 54,948 adolescents who were middle- and high-school students. Adolescents with potentially risky smartphone use showed a higher likelihood of suicidal ideation (OR: 1.50, CI: 1.42–1.60). Similarly, adolescents with high-risk smartphone use showed a significant risk of suicidal ideation (OR: 2.49, CI: 2.21–2.81) and suicide attempt (OR: 1.87, CI: 1.48–2.37) compared to the adolescents who were general users. Conclusion: Our study results encourage parents and social workers to acknowledge that adolescents’ smartphone addiction leads to a higher risk to their mental health, wherein they may engage in suicidal ideation and even resort to a suicide attempt.