Neuromorphic engineering aims to mimic brain functions to achieve energy‐efficient artificial intelligence. Since researchers have indicated that memristors can mimic synapses and neurons, various studies have demonstrated the operation of neural networks using memristive dot product engine (MDPE) hardware. However, although several feasible implementations of synapse and neuron behaviors have been reported, few studies have demonstrated the system‐level energy‐efficient operation on the hardware. This work proposes a novel system inspired by the neuromodulation of the brain, referred to as a “stashing system.” In the system, the trained synapses are stashed temporarily during the training of the spiking neural network and then merged for inferencing. The software simulation first confirmed the working principle of the stashing system. Then, a hardware demonstration is performed at an integrated 32 × 32 MDPE embodying a self‐rectifying and electroforming‐free memristor cell to validate the system. The results confirm that energy consumption in the memristor array is reduced by 37% for the unsupervised learning of the MNIST dataset.