As a promising candidate for high-density data storage and neuromorphic computing, cross-point memory arrays provide a platform to overcome the von Neumann bottleneck and accelerate neural network computation. In order to suppress the sneak-path current problem that limits their scalability and read accuracy, a two-terminal selector can be integrated at each cross-point to form the one-selector-one-memristor (1S1R) stack. In this work, we demonstrate a CuAg alloy-based, thermally stable and electroforming-free selector device with tunable threshold voltage and over 7 orders of magnitude ON/OFF ratio. A vertically stacked 64 × 64 1S1R cross-point array is further implemented by integrating the selector with SiO2-based memristors. The 1S1R devices exhibit extremely low leakage currents and proper switching characteristics, which are suitable for both storage class memory and synaptic weight storage. Finally, a selector-based leaky integrate-and-fire neuron is designed and experimentally implemented, which expands the application prospect of CuAg alloy selectors from synapses to neurons.