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In this work, Inconel 625 alloy is explored regarding high-temperature tensile deformation and fracture behaviors at a strain rate of 0.005–0.01 s−1 under a deformation temperature ranging from 700–800 °C. The subsequent analysis focuses on the impact of deformation parameters on flow and fracture characteristics. The fractured surface reveals that ductile fracture is dominated by the nucleation, growth, and coalescence of microvoids as the primary failure mechanisms. The elevated deformation temperature and reduced strain rate stimulate the level of dynamically recrystallized (DRX) structures, resulting in intergranular fractures. The Arrhenius model and the particle swarm optimization-artificial neural network (PSO-ANN) model are developed to predict the hot tensile behavior of the superalloy. It indicates that the PSO-ANN model exhibits a correlation coefficient (R) as high as 0.9967, surpassing the corresponding coefficient of 0.9344 for the Arrhenius model. Furthermore, the relative absolute error of 9.13% (Arrhenius) and 1.85% (PSO-ANN model) are recorded. The developed PSO-ANN model accurately characterizes the flow features of the Inconel 625 superalloy with high precision and reliability.