Chimeric antigen receptor T (CAR T) cell therapy has shown remarkable success in treating various leukemias and lymphomas. Cellular kinetic (CK) and pharmacodynamic (PD) behavior of CAR T cell therapy is distinct from other therapies due to its living nature. CAR T CK is typically characterized by an exponential expansion driven by target binding, fast initial decline (contraction), and slow long-term decline (persistence). Due to the dependence of CK on target binding, CK and PD of CAR T therapies are inherently and bidirectionally linked. In this work, we develop a semi-mechanistic model of CAR T CK/PD, incorporating molecular-scale binding, T cell dynamics with multiple phenotypes, and tumor growth and killing. We calibrate this model to published CK and PD data for a CD19-targeting CAR T cell therapy. Using sensitivity analysis, we explore variability in response due to patient- and drug-specific properties. We further explore the impact of tumor characteristics on CAR T-cell expansion and efficacy through individual- and population-level parameter scans.