Previous high-throughput evaluations of CRISPR activities for a large number of target and guide RNA sequences were based on measuring insertion-deletion frequencies rather than cleavage efficiencies. Here we develop two high-throughput in vitro methods, Cut-seq1 and Cut-seq2, to evaluate Cas9 cleavage efficiency for tens of thousands, or even hundreds of thousands, of guide RNA-target pairs. These methods reveal low correlations between in vitro cleavage efficiencies and insertion-deletion frequencies in cells, yet high concordances in protospacer adjacent motif compatibility. Using the resulting large datasets of in vitro cleavage efficiencies, we develop DeepCut, a set of deep learning models that can identify optimized single-guide RNAs that can selectively cleave specific sequences, even in the presence of similar noise sequences. Using these optimized single-guide RNAs, we develop a method, CLOVE-seq (which stands for cleavage for large-scale optimized variant enrichment sequencing), to enrich rare variants in a multiplexed manner by Cas9-mediated specific cleavage of noise or rare variant sequences. Our methods can enhance the understanding of CRISPR nuclease activities and could be used to detect a large number of rare variants in various biomedical contexts.