Cardiac perfusion is governed by fluid transport through a deformable porous myocardium and is strongly coupled with tissue mechanics. Accurate numerical simulation of this process is essential for understanding physiological perfusion as well as pathological conditions such as ischemia and microvascular dysfunction. However, fully coupled poromechanical models of cardiac perfusion pose significant computational challenges due to nonlinear solid deformation, strong multiphysics coupling, and the large-scale three-dimensional domains required for realistic simulations. This work presents a matrix-free finite element framework for poromechanical cardiac perfusion, specifically designed for large-scale high-performance computing applications. The governing equations are formulated within a poromechanical framework, coupling nonlinear myocardial deformation with fluid mass conservation and permeability-driven transport in the deformable porous myocardium. Spatial discretization is based on the finite element method, while all linearized operators are applied in a matrix-free manner, thereby avoiding the explicit assembly and storage of global system matrices. This formulation substantially reduces memory requirements and improves arithmetic intensity, making it well-suited for modern many-core and distributed-memory architectures. Efficient matrix-free operator evaluation, scalable solver and preconditioning strategies, and parallel implementation aspects are discussed. Numerical examples on organ-scale myocardial perfusion, representative of left ventricular flow, demonstrate the accuracy, robustness, and parallel scalability of the proposed framework for large-scale cardiac perfusion simulations on modern high-performance computing platforms. The results indicate that the matrix-free formulation enables high-resolution perfusion modeling at a computational cost that would be prohibitive for conventional matrix-based methods.