Recent advancements in computational biology have ushered in a new phase of precision medicine by enabling highly accurate simulations of cancer tumor progression. This study introduces a cutting-edge biphasic tumor growth model based on continuum mechanics, incorporating key interactions within the tumor microenvironment (TME), including immune system dynamics and anti-PDL1 immunotherapy, within a stochastic framework. Given the uncertainty in critical model parameters, a Bayesian inference approach is employed to derive their probabilistic characteristics from available data. The computational complexity arising from the coupled, nonlinear partial differential equations (PDEs) governing the model is efficiently managed using a Deep Operator Network (Deep-O-Net) surrogate model. This integration drastically reduces computational costs in the context of uncertainty quantification (UQ) while maintaining high accuracy in predicting the stochastic behavior of tumor response. By facilitating robust parameter estimation under uncertainty, this framework underscores the significance of probabilistic modeling in cancer research and demonstrates its adaptability for a broad spectrum of TME-centered therapeutic approaches.