Designing a composite, possibly strengthened by a dispersion of (fine) oxides, is a favorable way to improve the mechanical characteristics of Cu while maintaining its advantageous electric conductivity. The aim of this study was to perform mechanical alloying of a Cu powder with a powder of Al2O3oxide, seal the powder mixture into evacuated Cu tubular containers, i.e., cans, and apply gradual direct consolidation via rotary swaging at elevated temperatures, as well as at room temperature (final passes) to find the most convenient way to produce the designed Al2O3particle-strengthened Cu composite. The composites swaged with the total swaging degree of 1.83 to consolidated rods with a diameter of 10 mm were subjected to measurements of electroconductivity, investigations of mechanical behavior via compression testing, and detailed microstructure observations. The results revealed that the applied swaging degree was sufficient to fully consolidate the canned powders, even at moderate and ambient temperatures. In other words, the final structures, featuring ultra-fine grains, did not exhibit voids or remnants of unconsolidated powder particles. The swaged composites featured favorable plasticity regardless of the selected processing route. The flow stress curves exhibited the establishment of steady states with increasing strain, regardless of the applied strain rate. The electroconductivity of the composite swaged at elevated temperatures, featuring homogeneous distribution of strengthening oxide particles and the average grain size of 1.8 µm2, reaching 80% IACS (International Annealed Copper Standard).