The effect of axial traverse speed of friction stir back extrusion (FSBE) process on the microstructure, mechanical, electrical, and wear properties of Cu−Ti2SnC composite wire was investigated. The FSBE process was performed on the primary composite made by the powder metallurgy method with 5 vol.% of Ti2SnC MAX phase. The results showed that as the extrusion speed increased, the twins formed in the microstructure increased, the Ti2SnC particles became finer, and the interface of bonding of the MAX phase−Cu matrix improved. The Cu−Ti2SnC composite wire fabricated at the rotational speed of 600 r/min and axial traverse speed of 25 mm/min showed the maximum hardness, yield strength, and ultimate tensile strength of HV 132.7, 278.34 MPa, and 485.15 MPa, respectively. This finding was due to its strong interfacial bonding and fine MAX phase particles. Besides, the larger grain size, the better interface bonding, and the lower the porosity resulted in the highest electrical conductivity of 89.21% (IACS) and least wear rate of 0.0015 mg/m of Cu−Ti2SnC composite wire fabricated at rotational speed of 600 r/min and axial traverse speed of 25 mm/min.