Suicide is a major public health problem, and it is urgent to investigate its underlying clinical and psychological concomitants. It has been suggested that low mentalization skills and problematic use of the internet (PUI) are factors that can play a role in suicidal behaviors. It is possible that poor mentalization skills contribute to leading to forms of PUI, which, in turn, can represent triggers for suicidal ideation (SI). We tested this hypothesis through a quantitative and cross-sectional study on a sample (n = 623) of young adults (age range: 18–34). Self-report measures investigating symptoms related to Social Media Addiction (SMA), Internet Gaming Disorder (IGD), mentalization capacity, and SI were used. A single mediation analysis with two mediators was carried out to evaluate the direct and indirect effects of mentalization on SI through the mediating role of SMA- and IGD-related symptoms, controlling for potential confounding factors (e.g., socio-demographic and addiction-related variables). The four explored variables were significantly associated with each other (all p < 0.001) across all subjects; the mediational model showed that the total effect of mentalization on SI was significant (B = −0.821, SE = 0.092 (95% CI: −1.001; −0.641)) and that both SMA- (B = −0.073, SE = 0.034 (95% CI: −0.145; −0.008)) and IGD-related symptoms (B = 0.046, SE = 0.027 (95% CI: −0.107; −0.001)) were significant mediators of such association. Our findings support the possibility that PUI severity plays a relevant role in mediating the association between low mentalization skills and levels of SI.