MXenes have shown great potential application in new electronic devices owing to the unique surface properties and 2D structure, especially in the popular memory storage. In this work, Ti₃C₂T_x, one of the MXenes, is partially oxidized and used as the resistance layer to fabricate memristors with resistance switching characteristics and synapse characteristics. The device exhibits excellent bipolar resistance switching property based on the gradual formation and annihilation of the conductive filaments of oxygen vacancy cation, including enough on/off ratio (≈10²), long cyclic endurance (>10³ cycles) and retention time (>10⁴ s). Furthermore, since oxygen vacancy cation migration is similar to the Ca²⁺ ion dynamics of biological synapses, the device successfully mimics biological synaptic functions such as paired-pulse facilitation (PPF), long-term potentiation (LTP) and long-term depression (LTD). This work provides the experimental and theoretical foundation for MXenes in memristor and artificial synapse filed, pushes the development of MXenes in neurocomputing application.