Toehold-mediated strand displacement (TMSD) as an important player in DNA nanotechnology has been widely utilized for engineering non-enzymatic molecular circuits. However, these circuits suffer from uncontrollable leakage and unsatisfactory response speed. We utilized site-specific and sequence-independent nucleases to engineer high- robustness DNA molecular circuits. First, we found that the kinetics of the APE1-catalyzed reaction is highly dependent on substrate stability, allowing for the elimination of asymptotic leakage of DNA split circuits. Second, we obtained strict substrate preference of λ exonuclease (λexo) by optimizing the reaction conditions. Robust single-layer and cascade gates with leak resistance were established by using λ exo. Owing to the remarkably fast kinetics of these nucleases, all the circuits yield a high speed of computation. Compared to TMSD-based approaches, nuclease-powered circuits render advanced features such as leakage resistance, hundreds of times higher speed, and simplified structures, representing a class of promising artificial molecule systems.