In our previous study, we observed that the Mg_97.37Zn_1.88Y_0.75 (at%) alloy, composed of α-Mg, the W phase (Mg₃Zn₃Y₂), and a small quantity of the I phase (Mg₃Zn₆Y) exhibited an extremely high thermal conductivity of 141 Wm^-1K^-1 attributable to the precipitation of a large amount of the fine W phase through heat treatment at 633 K for 15 h. In the present study, we examined how extrusion conditions affect the thermal conductivity and mechanical properties of the Mg_97.37Zn_1.88Y_0.75 alloy with high thermal conductivity. As a result, an extruded Mg alloy was developed, exhibiting excellent properties, including a thermal conductivity of 131 Wm^-1K^-1, a tensile strength of 361 MPa, and an elongation of 9.7%. These superior mechanical properties were obtained by optimizing extrusion conditions, thereby inducing dynamic recrystallization during the process to refine the α-Mg matrix and causing the dynamically recrystallized area, which consisted of grains with lower strain and random orientation, to expand. Furthermore, a decline in thermal conductivity by 9–11 Wm^-1K^-1 was observed following extrusion, independent of the specific processing parameters.