Synthetic biological circuits are designed to regulate gene expressions to control cell function. To date, these circuits often use DNA-delivery methods, which may lead to random genomic integration. To lower this risk, an all RNA system, in which the circuit and delivery method are constituted of RNA components, is preferred. However, the construction of complexed circuits using RNA-delivered devices in living cells has remained a challenge. Here we show synthetic mRNA-delivered circuits with RNA-binding proteins for logic computation in mammalian cells. We create a set of logic circuits (AND, OR, NAND, NOR, and XOR gates) using microRNA (miRNA)- and protein-responsive mRNAs as decision-making controllers that are used to express transgenes in response to intracellular inputs. Importantly, we demonstrate that an apoptosis-regulatory AND gate that senses two miRNAs can selectively eliminate target cells. Thus, our synthetic RNA circuits with logic operation could provide a powerful tool for future therapeutic applications.