Concerns over the coronavirus disease 2019 (COVID-19) pandemic and control measures have affected the routine outpatient visits of individuals with comorbidities and their mental well-being. From October 2019 to August 2020, this cross-sectional study enrolled 135 patients who sought medical attention at a medical center in Taiwan. This period covered the early (October to December 2019), peak (January to April 2020), and late (May to August 2020) periods of the COVID-19 outbreak in Taiwan. The demographic data, social support data, activities of daily living (ADL), resilience scale scores, and mental well-being scale scores of the participants were compared. There were no statistically significant differences in the participation rate, demographic data, and social support data between the three periods. The correlation analysis confirmed significant negative relationships between the number of COVID-19 cases and outpatient department visits per month (r = −0.764, p < 0.001), emergency department visits per month (r = −0.023, p < 0.001), ADL (r = −0.257, p = 0.03), resilience scale (r = −0.390, p < 0.001), and mental well-being scale (r = −0.475, p < 0.001). In conclusion, the severity of the COVID-19 outbreak in Taiwan was associated with declines in the ADL, mental well-being, and resilience of patients who sought medical attention.