Memristive devices based on high-temperature superconducting cuprates offer promising routes for neuromorphic computing, yet the microscopic mechanisms governing their resistive switching remain unclear. Here we investigate YBa₂Cu₃O_7−δ (YBCO) memristors across 80–300 K, revealing robust bipolar switching between high- and low-resistance states with temperature-independent SET and RESET voltages. Current–voltage analysis shows both states follow trap-controlled space-charge-limited conduction, modulated by shallow and deep trap states at an oxygen-deficient interfacial YBCO layer. A key enabler of this behavior is the formation of a deoxygenated layer beneath the top contact, which acts as a dynamic trap region and allows electrostatic control over a field-induced metal–insulator transition. We propose a dual-trap model where deep traps linked to CuO chain fragmentation stabilize a field-induced metal–insulator transition, enabling nonvolatile switching. These insights elucidate the role of trap dynamics in cuprate memristors and highlight their potential for cryogenic neuromorphic platforms compatible with superconducting computing architectures.