A novel concept of the turbo-piston combined cycle (TPCC) engine was proposed to perfectly satisfy the complex and multiple performance requirements of many heavy vehicles. It has a unique function of free mode (cycle) switching between three operating modes, which are the diesel engine (DE), the turboshaft engine (TE), and the DE–TE cyclic combined modes. The cyclic coupling between the baseline DE and TE cycles in the combined mode was supposed to help improve the performances of the two baseline engines simultaneously, and prototype experiments confirmed the feasibility and effects of this assumption. However, the cyclic coupling mechanisms in the combined cycle that are crucial for the R&D of the TPCC engine remain unclear. This study mainly focuses on investigating the fundamentals of the cyclic coupling mechanisms and impacts in the combined cycle of the TPCC engine via theoretical (ideal) thermodynamic cycle modeling analysis and one-dimensional (1-D) cycle modeling simulation. The results mainly show that from theoretical thermodynamic analysis, the TPCC engine’s cyclic coupling can significantly improve the specific net work of the combined cycle and even exceed the sum of the isolated DE and TE cycles, and only the temperature increase ratio parameter of the TE cycle can generate a tradeoff influence between the specific net work and the theoretical thermal efficiency of the combined cycle. In addition, from the 1-D cycle simulation, the performance of the baseline DE cycle in the combined cycle is dramatically improved by the baseline TE in terms of its high intake pressure and exhaust pressure conditions, and the operating process of baseline TE is simultaneously improved by the baseline DE in terms of its intake suction and exhaust-mixing effects. Based on certain simulation cases, the intake mass flow rates of the baseline DE and TE (i.e., the total intake mass flow rate of the combined cycle) are respectively increased by 150% and 1.1%, and their power outputs are respectively increased by 8.5% and 3.1%. Further, the brake specific fuel consumption rate (BSFC) of the baseline DE and TE respectively decreases by 8.0% and 2.9%, and the operating point of the baseline TE on the turbomachinery performance maps is slightly moved to the more efficient and higher performance area. This investigation is consistent with experimental results on cyclic coupling effects, and it can provide a timely and preliminarily understanding of the TPCC engine’s fundamentals.