Ti-6Al-4V is an alloy that has a high strength-to-weight ratio. It is known as an alpha-beta titanium alloy with excellent corrosion resistance. This alloy has a wide range of applications, e.g., in the aerospace and biomedical industries. Examples of alpha stabilizers are aluminum, oxygen, nitrogen, and carbon, which are added to titanium. Examples of beta stabilizers are titanium–iron, titanium–chromium, and titanium–manganese. Despite the exceptional properties, the processing of this titanium alloy is challenging when using conventional methods as it is quite a hard and tough material. Nonconventional methods are required to create intricate and complex geometries, which are difficult with the traditional methods. The present study focused on machining Ti-6Al-4V using wire electrical discharge machining (WEDM) and conducting numerous experiments to establish the machining parameters. The optimal setting of the machining parameters was predicted using a multiresponse optimization technique. Experiments were planned using the response surface methodology (RSM) technique and analysis of variance (ANOVA) was used to determine the significance and contribution of the input parameters to changes in the output characteristics (cutting speed and surface roughness). The cutting speed obtained during the processing of the annealed titanium alloy using WEDM was quite large as compared to the cutting speed obtained in the case of processing the pure, quenched, and hardened titanium alloys using WEDM. The maximum cutting speed obtained while processing the annealed titanium alloy was 1.75 mm/min.