In this paper, a novel method of cryogenically cooled (low-temperature nitrogen gas) wire tool is used during the oxygen-mist near-dry wire-cut electrical discharge machining (NDWEDM) process to cut Inconel 718 alloy material. The current, pulse-width, pulse-interval, and flow rate are the controllable variables for response characteristics, such as the material removal rate (MRR) and wire wear ratio (WWR). The Box-Behnken method is applied to design the experiments to collect the observations from experiments. The mathematical models for each response were developed using significant individual, interaction, and quadratic terms by the sequential sum of the square test. The response surfaces were developed. It was revealed from the analysis that 52.92 % of current, 24.63 % of Pulse-width, 12.81 % of pulse- interval and 5.75 % of flow rate contributed to MRR, while 14.89 % of current, 9.75 % of pulse-width, 62.20 % of pulse-interval, and 5.44 % of flow rate contributed to WWR. The pulse-width has more contribution on MRR due to the long period of spark between the wire and work materials. It was also observed that the pulse-interval has more effect on WWR due to the more ideal period (high spark-pause-time) between two consecutive high-temperature sparks in the wire tool. The wear of the wire tool has been analysed using scanning electron microscopy (SEM) photographs. The desirability principles were first applied to obtain multi-objective solutions with a combination of process parameters to achieve the optimal values of both responses. The predicted combination of results has been validated by data that were collected from confirmation experiments.