With thyroid cancer being a prevalent endocrine cancer, timely management is essential to prevent malignancy and detrimental outcomes. Surgical intervention is a popular component of the treatment plan, yet patients often refuse to undergo such procedures even if clinicians explicitly recommend them. This study gathers data from the Surveillance, Epidemiology, and End Results database (2000–2019) to learn more about the sociodemographic factors that predict the likelihood of surgical intervention. A total of 176,472 patients diagnosed with either papillary or follicular thyroid cancer were recommended surgery, of which 470 were refused. Cancer-specific mortality and overall mortality were determined with the Kaplan–Meier method and univariate and multivariate Cox proportional hazards regression model. Mortality rates for patients who delayed surgery (≥4 months vs. <4 months) were determined using similar methods. The findings reveal that surgical delay or refusal increased overall mortality. The surgical refusal was associated with increased thyroid cancer-specific mortality. However, the impact on thyroid cancer-specific mortality for those who delay surgery was not as pronounced. Significant sociodemographic determinants of surgical refusal included age greater than or equal to 55 years, male sex, being unmarried, race of Asian and Pacific Islander, and advanced tumor staging. The results underscore the importance of patient education, shared decision-making, and access to surgical interventions to optimize outcomes in thyroid cancer management.