Owing to the capability of integrating the information storage and computing in the same physical location, in-memory computing with memristors has become a research hotspot as a promising route for non von Neumann architecture. However, it is still a challenge to develop high performance devices as well as optimized logic methodologies to realize energy-efficient computing. Herein, filamentary Cu/GeTe/TiN memristor is reported to show satisfactory properties with nanosecond switching speed (<60 ns), low voltage operation (<2 V), high endurance (>104 cycles) and good retention (>104 s @85 °C). It is revealed that the charge carrier conduction mechanisms in high resistance and low resistance states are Schottky emission and hopping transport between the adjacent Cu clusters, respectively, based on the analysis of current-voltage behaviors and resistance-temperature characteristics. An intuitive picture is given to describe the dynamic processes of resistive switching. Moreover, based on the basic material implication (IMP) logic circuit, we proposed a reconfigurable logic method and experimentally implemented IMP, NOT, OR, and COPY logic functions. Design of a one-bit full adder with reduction in computational sequences and its validation in simulation further demonstrate the potential practical application. The results provide important progress towards understanding of resistive switching mechanism and realization of energy-efficient in-memory computing architecture.