The reversible switching of catalytic systems capable of performing complex DNA computing operations using the temporal control of two orthogonal photoswitches is described. Two distinct photoresponsive molecules have been separately incorporated into a split horseradish peroxidase-mimicking DNAzyme. We show that its catalytic function can be turned on and off reversibly upon irradiation with specific wavelengths of light. The system responds orthogonally to a selection of irradiation wavelengths and durations of irradiation. Furthermore, the DNAzyme exhibits reversible switching and retains this ability throughout multiple switching cycles. We apply our system as a light-controlled 4:2 multiplexer. Orthogonally photoswitchable DNAzyme-based catalysts as introduced here have potential use for controlling complex logical operations and for future applications in DNA nanodevices.