Young adults were vulnerable to mental health issues during the COVID-19 pandemic. However, the underlying pathway by which COVID-19-related stress influences mental health outcomes among young adults remains unclear. This study aimed to examine the mediating effects of social support and resilience between COVID-19-related stress and mental health outcomes. A sample of 1000 Korean young adults was obtained via online survey. Participants completed self-report questionnaires assessing COVID-19-related stress, social support, resilience, depression, and anxiety. Overall, 48.1% and 23.4% of participants were classified as having depression and anxiety states, respectively. Path analysis using AMOS version 26.0 (IBM Corp., Armonk, NY, USA) showed that the direct effects of stress from social distancing difficulties on depression and anxiety were much greater than those of stress from fear of infection and anger toward others. In addition, there were significant indirect effects of social support and resilience in the relationship between stress related to difficulties due to social distancing and mental health outcomes. The mediating roles of social support and resilience suggest that interventions to increase these factors can be effective strategies to reduce the risks of depression and anxiety among young adults suffering from stress related to social distancing difficulties.