In this study, a composite with alternate layers of 5056 and 1580 alloys was manufactured with wire arc additive manufacturing technology. It is shown that increased strength characteristics of composite material can be obtained with deformation treatment using a high-pressure torsion (HPT) technique. The microstructure and mechanical properties of the HPT-processed material in different structural states were investigated. The HPT-processed material exhibits a high value of ultimate tensile strength (~770 MPa) but low ductility. Short-term annealing at 250 °C and additional deformation with HPT to 0.25 of revolution at room temperature resulted in a slight decrease in the material’s strength to ~700 MPa but provided ductility of ∼9%. Physical mechanisms to improve plasticity in correlation with microstructure evolution are discussed.