The use of TI-6AL-4V alloy is increasing in various industries, due to its characteristics such as high strength to weight ratio and excellent creep and corrosion resistance. However, because of titanium alloys poor machinability, non-traditional machining is usually used in shaping them. In this research, the wire cut machining of Ti-6Al-4V alloy has been investigated. In this regard, the effects of 8 process parameters and their optimal values are determined, for two process characteristics, cutting rate and surface roughness. One of the innovative aspects of the current study is the consideration of cutting height as one of the main parameters affecting the process output quality. Therefore, for three different cutting heights (each with two replicates), the L18 Taguchi matrix is employed to gather the required experimental data. Then, using the 108 data, statistical analysis, including signal to noise and analysis of variance were carried out in order to determine optimal process parameters and their effects on the two process outputs. Optimal process parameters values for maximum cutting rate and minimum surface roughness were verified by validation experiments. The results illustrate that the cutting height would alter the effects of process parameters and their optimal values. Finally, multi-objective optimization was performed to determine optimal parameters settings based on relative importance of process outputs for cutting heights of 30, 60 and 90 mm, in the form of technology table. The contribution of uncontrolled parameters and errors were less than 10% in all cases, which indicate the accuracy of the proposed technique.