As mentioned in the literature, SPS (Spark Plasma Sintering) technology combines uniaxial charge and pulsed currents to achieve the rapid sintering of powders. Although the utilization of current is often reported, an understanding of its role in the sintering mechanisms is still a subject of controversy. In fact, the oxide layer around metal particles is sometimes considered to be a dielectric gap in which discharges may occur: these discharges can clean the surface of particles and enhance densification. In this paper, an oxide layer was grown on the particle surface of a copper powder, and the growth enabled the study of the role of current on such dielectric layers. The powders were sintered by SPS using graphite tools in a reference cycle with constant current and a relatively low pressure of 4 MPa to limit the plastic deformation of particles. Three sintering configurations were compared to this reference experiment: (i) one without current in a HP process, (ii) one with a strongly pulsed current using graphite and alumina tools and (iii) one with a high heating rate. The results indicate that current does not alter the sintering mechanism. No cleaning effect of the particle surface was observed. The oxide layers remain in the sintered samples and form collars around the necks. The oxide layer modifies the sintering mechanism; it leads to the delay of consolidation phenomena on the surface.