The increasing demand for orthogonal cutting in the machining of difficult-to-cut materials may be ascribed to its superior benefits. These advantages can be achieved by using several hybrid machining techniques such as laser assisted machining. The utilisation of laser technology in machining processes is considered to be a sophisticated method for the processing of materials that are difficult to cut. The present study involves the utilisation of a Nd:YAG laser source to preheat a Nitinol shape memory alloy (SMA) work piece, which was subsequently subjected to machining using a laser-assisted Computer numerical control (CNC) turning centre varying various machining conditions. Furthermore, statistical techniques such as the Response Surface Method (RSM), Adaptive Neurofuzzy Inference System (ANFIS), and Artificial Neural Networks (ANN) with Back Propagation (BP) algorithm-based numerical modelling are employed to find the impact of different parameters such as cutting speed, feed, cutting depth, and laser power on the response variables i.e. cutting force (Fz) and surface roughness (SR). The results of the ANOVA analysis indicate that the cutting speed is the primary factor that significantly affects both Fz and SR with 31.39% and 60.36% respectively. The outcomes of Fz and SR anticipated by RSM, ANFIS, and ANN exhibited a high degree of agreement with the empirical findings. It was found that the ANFIS method exhibited superior performance in terms of the machining responses when compared to RSM and ANN. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.