This paper proposes a novel multi-stage heuristic method for solving the Security-Constrained Unit Commitment (SCUC) problem in hydro-thermal power systems. Due to the large-scale nature and non-convexity of SCUC, it is computationally challenging to solve it directly as a Mixed Integer Programming (MIP) model. We propose a novel heuristic approach to expedite the solving process, significantly reducing computational cost whilst preserving high solution quality. By strategically combining Lagrangian relaxation and MIP techniques, our approach iteratively relaxes complex constraints and uses solutions from relaxed problems to guide variable fixing in subsequent stages. Numerical experiments demonstrate that our proposed method achieves solutions nearly identical to those of state-of-the-art MIP solvers, whilst significantly reducing solving times by more than 50%. These results highlight the potential of our heuristic approach in enhancing power system operational efficiency and reliability.