Deoxyribozymes (DNAzymes) are single-stranded DNA that catalyze nucleic acid biochemistry. Although a number of DNAzymes have been discovered by in vitro selection, the relationship between their tertiary structure and function remains unknown. We focus here on the well-studied 10-23 DNAzyme, which cleaves mRNA with a catalytic efficiency approaching that of RNase A. Using coarse-grained Brownian dynamics simulations, we find that the DNAzyme bends its substrate away from the cleavage point, exposing the reactive site and buckling the DNAzyme catalytic core. This hypothesized transition state provides microscopic insights into experimental observations concerning the size of the DNAzyme/substrate complex, the impact of the recognition arm length, and the sensitivity of the enzymatic activity to point mutations of the catalytic core. Upon cleaving the pertinent backbone bond in the substrate, we find that the catalytic core of the DNAzyme unwinds and the overall complex rapidly extends, in agreement with experiments on the related 8-17 DNAzyme. The results presented here provide a starting point for interpreting experimental data on DNAzyme kinetics, as well as developing more detailed simulation models. The results also demonstrate the limitations of using a simple physical model to understand the role of point mutations.