In this work, a dynamic model is proposed to simulate the drilling and steering process of an autonomous burrowing mole to access scientific samples from the deep subsurface of the Moon. The locomotive module is idealized as a rigid rod. The characteristic parameters are considered, including the length, cross-section diameter, and centroid of a cylindrical rod. Based on classical Lagrangian mechanics, a 3-DOF dynamic model for the locomotion of this autonomous device is developed. By introducing resistive force theory, the interaction scheme between the locomotive body and the lunar regolith is described. The effects of characteristic parameters on resistive forces and torques are studied and discussed. Proportional-derivative control strategies are introduced to calculate the tracking control forces following a planned trajectory. The simulation results show that this method provides a reliable manipulation of a mole-type robot to avoid obstacles during the tracking control process in layered sediments. Overall, the proposed reduced-order model is able to simulate the operating and controlling scenarios of an autonomous burrowing robot in lunar subsurface environments. This model provides intuitive inputs to plan the space missions of a drilling robot to extract subsurface samples on an extraterrestrial planet such as the Moon or Mars.