The SpCas9 endonuclease has become an important tool in gene-editing and basic science alike. Though easily programmed to target any sequence, SpCas9 also shows considerable activity over genomic off-targets. Many empirical facts regarding the targeting reaction have been established, but a comprehensive mechanistic description is still lacking—limiting fundamental understanding, our ability to predict off-target activity, and ultimately the safe adaptation of the SpCas9 toolkit for therapeutics. By mechanistically modelling the SpCas9 structure-function relationship, we simultaneously capture binding and cleavage dynamics for SpCas9 and Sp-dCas9 in terms of free-energies. When our model is trained on high-throughput data, we outperform state-of-the-art off-target prediction tools. Based on the biophysical parameters we extract, our model predicts the open, intermediate, and closed complex configurations described in single-molecule FRET experiments, and indicates that R-loop progression is tightly coupled to structural changes in the targeting complex. We further show that SpCas9 targeting kinetics are tuned for extended sequence specificity while maintaining on-target efficiency. Our approach can be used to characterize any other CRISPR derived nuclease, and contrasting future studies of high-fidelity variants with the SpCas9 benchmark we here provide will help elucidate the determinants of CRISPR fidelity and the path to increased specificity and efficiency in engineered systems.