The printed circuit heat exchanger (PCHE) with arrayed microchannel structures is ideal for the extreme thermal management of hypersonic flight vehicles. Electrically assisted manufacturing (EAM) has a remarkable predominance in fabricating microchannels on sheet metals. By conducting EA micro-embossing experiments at current densities of 20, 25, and 40 A/mm2, respectively, the filling behavior and microstructural evolution of SUS304 sheets under the influence of current were elucidated in this study. The results indicated that a higher current density shortens the initial extrusion stage's duration and facilitates the material flow transition to the filling stage. Moreover, the current can simultaneously enhance the filling height and profile quality by minimizing the stress and stress differential in the deformation region of the filling section. The results of electron backscatter diffraction (EBSD) demonstrated that recrystallization occurs due to the synergistic effect of deformation and current. The degree of recrystallization in different regions of the filling section has a huge discrepancy. The region beneath the tooth exhibits considerable recrystallization and contains abundant refined grains. At the current density of 20 A/mm2, a number of dislocations accumulated in the deformed grains, and the filling section mainly consisted of 〈1 1 1〉 fiber texture and 〈1 0 1〉 deformation texture. In the process of continual dynamic recovery and recrystallization, dislocation packing relives at the current density of 40 A/mm2, which is one reason for the increase in filling quality. The 〈1 1 1〉 texture and 〈1 0 1〉 deformation texture are weakened and rotate as the forming temperature rises. Additionally, the 〈1 0 1〉 texture transforms into a 〈0 0 1〉 recrystallized texture. The diminished 〈1 0 1〉 deformation texture, the rotated 〈1 1 1〉 texture, and the appearance of 〈0 0 1〉 recrystallized texture enhance the homogenous strain distribution of the filling section, which is an additional explanation for the improvement of filling quality at high-density current. Based on the above results, a high-performance PCHE prototype with a pressure bearing capacity of 23 MPa and a heat transfer coefficient of 22 kW/(m2·K) was manufactured by EAM, confirming that the EAM technique is capable of achieving high-quality and eco-friendly fabrication of the enhanced microchannels.