Based on biochemical characteristics of lymphocytes in immune responses, the competition between tumor and immune system should be divided into two stages, namely immature lymphocytes which are incapable to kill the tumor cells, and mature lymphocytes which can effectively kill the tumor cells. Therefore, the evolution law of the two-stage tumor-immune model is discussed from deterministic and random perspectives, respectively. Based on stability and phase diagram analysis, it is found that the tumor-free equilibrium point can achieve asymptotical stability, and the tumor can be completely eliminated. However, the tumor-present equilibrium point is unstable. In this case, immune cells and tumor cells will keep competing with each other in the long run. Considering influence caused by the microenvironment of cells growth, Gaussian white noise near the steady-state equilibrium on the mean values and second moments of cell density are studied. It is found that the microenvironment noise changes evolution of tumor cell near the first equilibrium, indicating that the microenvironment here is conducive to survival and growth of tumor. The second-moment curves illustrate fluctuation of all the tumor cell density due to the influence of microenvironment. Comparatively, tumor cell density fluctuates greatly around the second equilibrium, but it is less affected by the microenvironmental noise. In addition, both immature lymphocytes and tumor cells are non-linearly sensitive to the kill rate parameter of the immune system.