<p>This paper introduces a new nonparametric estimator for the bivariate distribution function based on Szász–Mirakyan operators, providing the first systematic framework for applying approximation-theoretic methods to censored multivariate survival data. The proposed estimator naturally accommodates non-negative lifetimes and avoids boundary bias, while retaining smoothness and flexibility. We derive its large-sample properties, including consistency, a decomposition of the bias–variance structure, and an asymptotically optimal smoothing parameter that depends on the effective sample size under censoring. Simulation studies demonstrate that the estimator achieves lower mean squared error than classical methods, with particular gains under moderate censoring and strong dependence. A real-data application further illustrates the practical stability and interpretability of the approach. Overall, the results show that Szász–Mirakyan operators offer a powerful and versatile tool for nonparametric estimation of bivariate distributions in the presence of censoring.</p>