Bacterial CRISPR-Cas systems comprise diverse effector endonucleases with different targeting ranges, specificities and enzymatic properties, but many of them are inactive in mammalian cells and are thus precluded from genome-editing applications. Here we show that the type II-B FnCas9 from Francisella novicida possesses novel properties, but its nuclease function is frequently inhibited at many genomic loci in living human cells. Moreover, we develop a proximal CRISPR (termed proxy-CRISPR) targeting method that restores FnCas9 nuclease activity in a target-specific manner. We further demonstrate that this proxy-CRISPR strategy is applicable to diverse CRISPR-Cas systems, including type II-C Cas9 and type V Cpf1 systems, and can facilitate precise gene editing even between identical genomic sites within the same genome. Our findings provide a novel strategy to enable use of diverse otherwise inactive CRISPR-Cas systems for genome-editing applications and a potential path to modulate the impact of chromatin microenvironments on genome modification.