CRISPR-Cas systems are adaptive immune systems protecting bacteria and archaea against intruding genetic elements. Of the different types, the signature nucleases of type II and type VA, Cas9 and Cas12a, are popular choices for gene editing since they are single proteins that can be redirected to cleave any site in the genome by simply changing the sequence of their guide RNA. This aspect has catapulted CRISPR-Cas systems into powerful gene editing tools, but the dearth in the knowledge of mechanisms of DNA cleavage by these proteins and their potential off-target effects have restricted their use as therapeutic medicine. As part of our study, we characterized mechanisms by which Cas9 and Cas12a cleave DNA, focusing on abilities to cleave DNA specifically and non-specifically. We identified a previously unknown activity in several Cas proteins where in DNA is cleaved non-specifically in the absence of a guide RNA. This activity needs specific divalent metal ions such as Mn2+ and Co2+ for increased efficiency. Protein engineering attempts are underway to remove this promiscuous DNA cleavage. With regard to increasing stringency of sequence-specific DNA cleavage catalyzed by Cas proteins, our studies established that a highly conserved alpha helix present in several families of Cas proteins can be modulated to increase cleavage stringency, thus reducing off-target cleavage during genome editing applications. Altogether, the mechanistic insights provided by the current study enables the development of safer CRISPR-based genome editing tools.