Cytotoxic T lymphocytes (CTLs) kill virus-infected cells and tumor cells, and play a critical role in immune protection. Our knowledge of how the CTL killing efficiency varies with CTL and target cell numbers is limited. Here, we simulate a region of lymphoid tissue using a cellular Potts model to characterize the functional response of CTL killing of target cells, and find that the total killing rate saturates both with the CTL and the target cell densities. The relative saturation in CTL and target cell densities is determined by whether a CTL can kill multiple target cells at the same time, and whether a target cell can be killed by many CTLs together. We find that all the studied regimes can be well described by a double-saturation (DS) function with two different saturation constants. We show that this DS model can be mechanistically derived for the cases where target cells are killed by a single CTL. For the other cases, a biological interpretation of the parameters is still possible. Our results imply that this DS function can be used as a tool to predict the cellular interactions in cytotoxicity data.