This talk presents a novel adaptive approach based on the smoothed particle hydrodynamics method to simulate the metal cutting process. The adaptive simulation includes two parts: a refinement algorithm to capture the large deformation and a coarsening algorithm to optimize the calculation time. The adjacent area where the workpiece and the tool are in contact is defined as the local critical region. During the cutting process, the number of particles inside the critical region increses dynamically, and the particles leaving the region are merged. A uniform distribution of position and mass of particles are adopted to ensure the conservation of the system. The modified Johnson-Cook model is selected for the material constitutive to describe the strain softening and energy transduction caused by the thermal-mechanical coupling. Numerical calculation is carried out under the updated Lagrangian framework. After a preliminary discussion of the particle distribution pattern, this work uses the dynamic variable resolution model and the preset multiple resolution model. The accuracy and effectiveness of the proposed techniques are verified through comparative analysis.