The cationic copolymer poly(L-lysine)-graft-dextran (PLL-g-Dex) has nucleic acid chaperone-like activity. The copolymer facilitates both DNA hybridization and strand exchange reactions. For these reasons, DNA-based enzyme (DNAzyme) activity is enhanced in the presence of copolymer. In this study, we evaluated activities of DNAzymes with substrate-binding arms (S-arms) of various lengths. The copolymer promoted DNAzyme reactivity and turnover efficacy, and, depending on S-arm length, maximally accelerated the reaction rate by 250-fold compared to the rate in the absence of copolymer. The copolymer permitted up to six nucleotides truncation of the S-arms having initial length of 10 and 11 nucleotides without loss of catalytic efficiency, enable tuning of the optimal temperature ranging from 30 to 55 °C. The approach might be useful for the development of DNAzyme systems targeting short or highly structured RNAs as well for improvement of DNAzyme-based nanomachines and biosensors.