The binary as-cast Al–Cu alloys Al-5%Cu, Al-25%Cu, and Al-33%Cu (in wt %), composed of the intermetallic θ-Al2Cu and α-Al phases, were prepared from pure components and were subsequently severely plastically deformed by extrusion combined with reversible torsion (KoBo) to refinement of α-Al and Al2Cu phases. The extrusion combined with reversible torsion was carried out using extrusion coefficients of λ = 30 and λ = 98. KoBo applied to the Al–Cu alloys with different initial structures (differences in fraction and phase size) allowed us to obtain for alloys (Al-25%Cu and Al-33%Cu), with higher value of intermetallic phase, large elongations in the range of 830–1100% after tensile tests at the temperature of 400 °C with the strain rate of 10−4 s−1. The value of elongation depended on extrusion coefficient and increase, with λ increasing as a result of α-Al and Al2Cu phase refinement to about 200–400 nm. Deformation at the temperature of 300 °C, independently of the extrusion coefficient (λ), did not ensure superplastic properties of the analyzed alloys. A microstructural study showed that the mechanism of grain boundary sliding was responsible for superplastic deformation.