Using electroslag welding to obtain Inconel 625 cladding can significantly reduce the manufacturing cost of products that require corrosion resistance. The constitutive model and cutting simulation of this widely used deposited metal were studied, which can help optimize machining parameters and reduce tool wear; the accuracy of the constitutive model describing the response of flow stress to strain, strain rate, and temperature is the basic requirement of cutting simulation accuracy, and the softening effect of temperature and strain rate coupling was determined by analyzing the stress–strain curves obtained by the split Hopkinson Pressure Bar experiment and the microstructure evolution of specimens before and after compression. A modified power-law constitutive model with high- and low-strain-rate sensitivity coefficients and softening term coupled with strain rate and temperature is established, and the prediction error is smaller than that of the original constitutive model. The cutting experiment with cutting oil was designed using the centroid composite face-centered design method. Based on the experimental data, the strain rate parameters, cut-off strain values, and friction coefficients required for the cutting simulation were obtained, and thermal property models were introduced into the cutting simulation. The average errors of the cutting force and feed force are 6.6 % and 6.9 %, respectively, which proves the reliability of the cutting simulation.