Dense silicon carbide/graphene nanoplatelets (GNPs) and silicon carbide/graphene oxide (GO) composites with 1 vol.% equimolar Y2O3–Sc2O3 sintering additives were sintered at 2000 °C in nitrogen atmosphere by rapid hot-pressing technique. The sintered composites were further annealed in gas pressure sintering (GPS) furnace at 1800 °C for 6 h in overpressure of nitrogen (3 MPa). The effects of types and amount of graphene, orientation of graphene sheets, as well as the influence of annealing on microstructure and functional properties of prepared composites were investigated. SiC-graphene composite materials exhibit anisotropic electrical as well as thermal conductivity due to the alignment of graphene platelets as a consequence of applied high uniaxial pressure (50 MPa) during sintering. The electrical conductivity of annealed sample with 10 wt.% of GNPs oriented parallel to the measuring direction increased significantly up to 118 S·cm−1. Similarly, the thermal conductivity of composites was very sensitive to the orientation of GNPs. In direction perpendicular to the GNPs the thermal conductivity decreased with increasing amount of graphene from 180 W·m−1 K−1 to 70 W·m−1 K−1, mainly due to the scattering of phonons on the graphene – SiC interface. In parallel direction to GNPs the thermal conductivity varied from 130 W·m−1 K−1 up to 238 W·m−1 K−1 for composites with 1 wt.% of GO and 5 wt.% of GNPs after annealing. In this case both the microstructure and composition of SiC matrix and the good thermal conductivity of GNPs improved the thermal conductivity of composites.