Experiencing HIV-related stigma has important impacts on the mental health of people living with HIV, which has implications for treatment adherence, disease progression, and health outcomes. The impacts of stigma are particularly important to consider among sexual and gender minorities, who often face a disproportionate burden of HIV. To address the implications of stigma in these key populations, we leveraged a longitudinal study conducted among Peruvian sexual and gender minorities to compare the relative effects of multiple mediators affecting the relationship between experienced HIV-related stigma and psychological distress: internalized HIV-related stigma, adaptive coping, and maladaptive coping. HIV-related stigma, coping, and distress were measured, respectively, at 24 weeks, 36 weeks, and 48 weeks post-diagnosis for 145 participants from the Sabes Study. HIV-related maladaptive coping largely mediated the relationship between experienced HIV-related stigma and distress. Our findings suggest interventions targeting maladaptive coping may alleviate the mental health consequences of experiencing HIV-related stigma.