RNA-cleaving DNAzymes hold great promise as gene silencers, and spatiotemporal control of their activity through site-specific reactions is crucial but challenging for on-demand therapy. We herein report a novel design of a bioorthogonally inducible DNAzyme that is deactivated by site-specific installation of bioorthogonal caging groups on the designated backbone sites but restores the activity via a phosphine-triggered Staudinger reduction. We perform a systematical screening for installing the caging groups on each backbone site in the catalytic core of 10-23 DNAzyme and identify an inducible DNAzyme with very low leakage activity. This design is demonstrated to achieve bioorthogonally controlled cleavage of exogenous and endogenous mRNA in live cells. It is further extended to photoactivation and endogenous stimuli activation for spatiotemporal or targeted control of gene silencing. The bioorthogonally inducible DNAzyme is applied to a triple-negative breast cancer mouse model using a lipid nanoparticle delivery system, demonstrating high efficiency in knockdown of Lcn2 oncogenes and substantial suppression of tumor growth, thus highlighting the potential of precisely controlling the DNAzyme functions for on-demand gene therapy.