In this work, a newly discovered biomedical grade Magnesium–Lithium–Strontium (Mg–Li–Sr) alloy is machined using electrochemical machining technology. Two main output constraints employed on the research project to evaluate machinability are surface roughness (Ra) and material removal rate (MRR). Changing feed rate (FR), current, electrolyte concentration (EC), and voltage is required in order to carry out experimental experiments. The trials were designed using the Taguchi method. The ANOVA findings show that current is the most significant factor, after voltage as the most significant input parameter in regulating Ra and MRR. The ideal parameter configuration for the CRITIC-linked Deng’s similarity approach method was 5 V, 1 A of current, 0.4 mm/min of FR, and 20 g/l of EC. The final product was a 0.0323 mm/min MRR and a 2.61 μm surface roughness. Furthermore, the response variables are anticipated using the adaptive neuro-fuzzy Inference System, which finally results in predictions that are very similar to the experimental results.