The automation of construction machinery is important for making construction more efficient. Simulations using digital twins, which replicate real construction sites, help achieve this goal. In particular, for analyzing excavation by hydraulic excavators, it is important to use a numerical method that accurately describes the large deformation of soil when interacting with a curved bucket and relates this behavior to the macroscopic properties of the soil. The Material Point Method (MPM) is a numerical method that combines particle and grid-based approaches, making it well-suited for large deformation problems of continua. However, conventional MPM treats kinematic variables at grid nodes as unknowns, which can cause volumetric locking when dealing with incompressible materials. This issue resembles the challenge faced by displacement-based finite element methods. Several countermeasures against the volumetric locking in MPM have been proposed. The B-bar method is one such technique, but its application to MPM has limitations. Specifically, the B-bar method evaluates volumetric strain at the element center, which may lead to errors if the element is only partially filled with particles. To overcome this problem, the authors introduced a mixed displacement-volumetric strain (u-εv) formulation to MPM that introduces volumetric strain as an additional nodal unknown. In this study, we performed excavation simulations using a combined framework of MPM with the u-εv formulation and Discontinuous Deformation Analysis (DDA), an implicit discontinuum-based analysis method. We validated our approach by comparing simulation results with two-dimensional model experiments using aluminum rods. We also compared our method with the B-bar method. The results showed that the u-εv formulation reduced the oscillations in the mean stress distribution that occurred with the B-bar method. Additionally, it reduced excessive particle outflow, leading to excavation resistance values that better matched the experimental results.