Nonproportional plastic deformations on the microscale are an emerging topic. A simplified theory of strain gradient elasto-plasticity is developed to study the evolution of yield strength in a copper wire sequentially experiencing tension and torsion. The pre-tension deformation and stress are inherited to the upcoming torsion process, resulting in a nonproportional loading condition. With consideration of the extra hardening effect due to strain gradient, pre-tension weakens the extra hardening effect of the strain gradient and the dependence on the wire radius. Cyclic torsion behavior is also investigated. Anomalous Bauschinger effect and plastic softening are found.