Nickel 200 is a commercially pure nickel alloy known for its excellent mechanical strength, corrosion resistance, and thermal stability, making it ideal for applications in aerospace, chemical processing, and power generation. However, its high toughness and work-hardening behavior make it a challenging material to machine using conventional methods. This study investigates the precision cutting characteristics of Nickel 200 using sinking electrical discharge machining (EDM). The purpose of this paper is to develop prediction models for an electrical discharge machining (EDM) process using mathematical models (linear, quadratic, and cubic) and artificial neural networks (ANN) and to determine which model is better at making accurate predictions. Peak current, pulse on time, and pulse off time were considered the main factors affecting volumetric material removal rate (MRR) and surface roughness (SR), which were evaluated as EDM performance characteristics. A series of experiments was conducted using cylindrical Nickel 200 specimens and copper electrodes, with kerosene as the dielectric fluid. The ANN model gives higher accuracy and precision compared to mathematical models for predicting MRR and SR in EDM machines. The ANN reached a total percentage error of approximately 1.10% for MRR and 0.48% for Ra, with R2 values of 99.25% and 99.20%, respectively, signifying superior model fit and generality. These results demonstrate the ANN model’s efficiency as a trustworthy and precise method for predicting EDM performance.