Irreversible destruction of disease-associated regulatory RNA sequences offers exciting opportunities for safe and powerful therapeutic interventions against human pathophysiology. In 2017, for the first time we introduced miRNAses–miRNA-targeted conjugates of a catalytic peptide and oligonucleotide capable of cleaving an miRNA target. Herein, we report the development of Dual miRNases against oncogenic miR-21, miR-155, miR-17 and miR-18a, each containing the catalytic peptide placed in-between two short miRNA-targeted oligodeoxyribonucleotide recognition motifs. Substitution of adenines with 2-aminoadenines in the sequence of oligonucleotide “shoulders” of the Dual miRNase significantly enhanced the efficiency of hybridization with the miRNA target. It was shown that sequence-specific cleavage of the target by miRNase proceeded metal-independently at pH optimum 5.5–7.5 with an efficiency varying from 15% to 85%, depending on the miRNA sequence. A distinct advantage of the engineered nucleases is their ability to additionally recruit RNase H and cut miRNA at three different locations. Such cleavage proceeds at the central part by Dual miRNase, and at the 5'- and 3'-regions by RNase H, which significantly increases the efficiency of miRNA degradation. Due to increased activity at lowered pH Dual miRNases could provide an additional advantage in acidic tumor conditions and may be considered as efficient tumor-selective RNA-targeted therapeutic.