Abstract: The selective degradation of disease-associated microRNA is promising for the development of new therapeutic approaches. In this study, we engineered a series of bulge-loop-forming oligonucleotides conjugated with catalytic peptide [(LeuArg)2Gly]2 (BC–miRNases) capable of recognizing and destroying oncogenic miR-17 and miR-21. The principle behind the design of BC–miRNase is the cleavage of miRNA at a three-nucleotide bulge loop that forms in the central loop region, which is essential for the biological competence of miRNA. A thorough study of mono- and bis-BC–miRNases (containing one or two catalytic peptides, respectively) revealed that: (i) the sequence of miRNA bulge loops and neighbouring motifs are of fundamental importance for efficient miRNA cleavage—i.e., motifs containing repeating pyrimidine–A bonds are more susceptible to cleavage; (ii) the incorporation of the second catalytic peptide in the same molecular scaffold increases the potency of BC–miRNase, providing a complete degradation of miR-17 within 72 h; (iii) the synergetic co-operation of BC–miRNases with RNase H accelerates the rate of miRNA catalytic cleavage by both the conjugate and the enzyme. Such synergy provides a rapid destruction of constantly emerging miRNA to maintain sufficient knockdown and achieve a desired therapeutic effect.