Entrapment and defeat are empirically-supported suicide risk factors. Their measurement is the subject of some debate, however. Also, limited work exists examining sexual and gender minority (SGM) differences in these suicide risk factors despite overall elevated rates of suicidal thoughts and behaviors (STBs) for SGM persons. The present study examined (1) entrapment and defeat differences by sexual orientation and gender identity, (2) factor structure and criterion validity of the Entrapment Scale (E-Scale) and the Defeat Scale (D-Scale), and (3) measurement invariance by sexual orientation (subsamples were too small for gender identity). A sample of 1,027 adults living in the United Kingdom completed a cross-sectional online questionnaire assessing mental health. Analysis of Variance and Kruskal-Wallis testing revealed: (1) all sexual minority (i.e., gay/lesbian, bisexual, and other SM) persons reported higher internal and external entrapment, defeat, and suicidal ideation compared to their heterosexual counterparts, and; (2) gender minority (i.e., transgender and gender diverse) persons reported higher internal and external entrapment, defeat, and suicidal ideation compared to cisgender persons. Supported by suicide theory, confirmatory factor analysis showed modest support for a two-factor E-Scale (internal and external), and a one-factor D-Scale. All entrapment and defeat scores displayed significant moderate positive correlations with suicidal ideation. E- and D-scale scores displayed high intercorrelation, tempering confidence in conclusions regarding the facture structure findings. Item threshold-level responding varied by sexual orientation for the D-Scale but not the E-Scale. Results are discussed with respect to suicide theory and measurement, public health, and clinical practice.