Engineered Streptococcus pyogenes (Sp) Cas9s and Acidaminococcus sp. (As) Cas12a (formerly Cpf1) improve cleavage specificity in human cells. However, the fidelity, enzymatic mechanisms, and cleavage products of emerging CRISPR nucleases have not been profiled systematically across partially mispaired off-target DNA sequences. Here, we describe NucleaSeq— nuclease digestion and deep sequencing—a massively parallel platform that measures cleavage kinetics and captures the time-resolved identities of cleaved products for more than ten thousand DNA targets that include mismatches, insertions, and deletions relative to the guide RNA. The binding specificity of each enzyme is measured on the same DNA library via the chip-hybridized association mapping platform (CHAMP). Using this integrated cleavage and binding platform, we profile four SpCas9 variants and AsCas12a. Engineered Cas9s retain wtCas9-like off-target binding but increase cleavage specificity; Cas9-HF1 shows the most dramatic increase in cleavage specificity. Surprisingly, wtCas12a—reported as a more specific nuclease in cells—has cleavage specificity similar to wtCas9 in vitro. Initial cleavage position and subsequent end-trimming vary across nucleases, guide RNA sequences, and position and base identity of mispairs in target DNAs. Using these large datasets, we develop a biophysical model that reveals mechanistic insights into off-target cleavage activities by these nucleases. More broadly, NucleaSeq enables rapid, quantitative, and systematic comparison of the specificities and cleavage products of engineered and natural nucleases.