Titanium alloy is a crucial structural material in the modern aerospace field due to its strong corrosion resistance and strength, low density, and reduced sensitivity to vibration load and impact load, as well as its ability to resist expansion in the case of cracks. However, during high-speed cutting of titanium alloy, it is prone to periodic saw-tooth chip formation, which can cause high-frequency fluctuations in the cutting force, aggravate the vibration of the machine tool system, and ultimately reduce the tool’s service life and the workpiece’s surface quality. In this study, we investigated the influence of the material constitutive law in modeling the Ti-6AL-4V saw-tooth chip formation and proposed a joint material constitutive law JC-TANH which was developed based on the Johnson–Cook constitutive law and the TANH constitutive law. It has two advantages of the two models (JC law and TANH law), which means that it can describe the dynamic properties accurately, the same as the JC model, not only under low strain but also under high strain. The most important thing is that it does not need to fit the JC curve at the early stage of strain changes. Additionally, we established a developed cutting model, which integrates the new material constitutive, and the improved SPH method to predict chip morphology, cutting and thrust forces which are collected by the force sensor; we also compared the data with experimental results. Experimental results show that this developed cutting model can better explain the shear localized saw-tooth chip formation and correctly estimate its morphology as well as the cutting forces.