Proper selection of cooling/lubricating technique is very important in the machining of difficult-to-cut materials such as nickel-based alloys due to their poor machinability. Among the available cooling/lubricating techniques, high-pressure jet-assisted machining offer remarkable opportunities in terms of increasing the productivity, reducing temperature in the cutting zone, excellent chip-breaking ability, and reduction of the costs associated with cooling/lubrication fluids. This article presents experimental investigation and multi-objective optimization of machining parameters of the high-pressure jet-assisted turning of Inconel 718 with coated carbide tools. The Taguchi L27 orthogonal array was used for the experimental design. Diameter of the nozzle, distance between the impact point of the jet and the cutting edge, pressure of the jet, cutting speed, and feed were considered as machining parameters. In order to optimize the six performance characteristics, namely cutting power, hydraulic power, material removal rate, surface roughness, cutting tool temperature, and chip length, Taguchi-based grey relational analysis and genetic algorithms were applied as multi-objective optimization approaches to identify the optimal levels of machining parameters. Moreover, the weights of the responses were determined by employing the analytic hierarchy process. Finally, a confirmation experiment with the machining parameters in their optimal levels was conducted with the aim to demonstrate the effectiveness of proposed multi-objective optimization approaches.