Shape Memory Alloys (often called SMAs) belong to a branch of alloys that “remember” their original shape. When the metals are twisted or disturbed from their initial shape, they are capable of coming back to their original shape on application of external stimuli such as magnetic field, heat or stress. Despite its widespread commercialization, Ni-Ti is considered a costly alternative. As a result, cost-effective and easy-to-process alloys such as Cu- and Fe-based alloys are currently being investigated. Processing of Fe-based alloys is difficult as their properties are texture dependant. Cu-based shape memory alloys are thus considered viable alternatives. So the unconventional machining operations like electrical discharge machining (EDM) and laser machining can also be used to manufacture Cu-based SMA components. But thermal machining operations like IBM (ion beam machining), EBM (electron beam machining), LBM (laser beam machining), PAM (plasma arc machining) and EDM (electrical discharge machining) removes material from the surface of the work piece through melting/vaporization. However, thermal damage such as theheat affectedzone is brought on by the intense heat flow in laser machining. Hence only a few works have been reported to differentiate and characterize the varied properties of the SMA machined through laser machining. This research work aims at optimizing the laser beam machining parameters and study its influence on surface characteristics and shape memory properties of Cu-based SMA. Based on the experiments carried out using L9 orthogonal array design matrix, optimal parameters were found out with response tables and graphs which is further analysed using grey relational analysis. Surface topography was analysed by scanning electron microscope (SEM). Differential scanning calorimetry (DSC) was used to investigate phase transformation temperatures and some thermodynamic parameters. X-Ray Diffraction (XRD) was also performed to find out the different phases that are present. The results showed the grey relational analysis coupled with Taguchi approach is an effective and convenient technique to optimize the laser machining parameters and achieve better results.