The Hodgkin-Huxley model for action potential generation in biological axons is central for understanding the computational capability of the nervous system and emulating its functionality. Owing to the historical success of silicon complementary metal-oxide-semiconductors, spike-based computing is primarily confined to software simulations and specialized analogue metal-oxide-semiconductor field-effect transistor circuits. However, there is interest in constructing physical systems that emulate biological functionality more directly, with the goal of improving efficiency and scale. The neuristor was proposed as an electronic device with properties similar to the Hodgkin-Huxley axon, but previous implementations were not scalable. Here we demonstrate a neuristor built using two nanoscale Mott memristors, dynamical devices that exhibit transient memory and negative differential resistance arising from an insulating-to-conducting phase transition driven by Joule heating. This neuristor exhibits the important neural functions of all-or-nothing spiking with signal gain and diverse periodic spiking, using materials and structures that are amenable to extremely high-density integration with or without silicon transistors.