Uncovering mechanisms and predicting tumor cell responses to CAR-NK cytotoxicity is essential for improving therapeutic efficacy. Currently, the complexity of these effector-target interactions and the donor-to-donor variations in NK cell receptor (NKR) repertoire require functional assays to be performed experimentally for each manufactured CAR-NK cell product and target combination. Here, we developed a computational mechanistic multiscale model which considers heterogenous expression of CARs, NKRs, adhesion receptors and their cognate ligands, signal transduction, and NK cell-target cell population kinetics. The model trained with quantitative flow cytometry and in vitro cytotoxicity data accurately predicts the short- and long-term cytotoxicity of CD33CAR-NK cells against leukemia cell lines across multiple CAR designs. Furthermore, using Pareto optimization we explored the effect of CAR proportion and NK cell signaling on the differential cytotoxicity of CD33CAR-NK cells to cancer and healthy cells. This model can be extended to predict CAR-NK cytotoxicity across many antigens and tumor targets.