In recent years, neuromorphic computing, inspired by the structure and function of biological nervous systems, has gained substantial attention. Memristors, which are capable of modulating conductivity via electric charge or magnetic flux, mimic synaptic interactions in the human brain, making them promising candidates for neuromorphic computing. This study proposes a method using femtosecond laser-processed graphene oxide memristors. Adjusting the scanning voltage at both device ends achieves polarity-controlled resistance switching. The device exhibits unipolar resistance switching at low voltages and stability over 150 cycles with a power consumption of only 0.75 nW. At higher voltages, bipolar switching occurs with increased conductivity over the test cycles. This study explores switching mechanisms under two voltage conditions, thus providing a comprehensive understanding of these mechanisms. This innovative approach using femtosecond laser-processed graphene oxide memristors shows promise for neuromorphic computing, offering efficient performance, stability, and adaptability across voltage scenarios.