Platelet plug formation is a critical physiological response to vascular injury, serving as a cornerstone of primary hemostasis. Understanding and simulating this process are essential for advancing patient-specific treatments and interventions. However, achieving a balance between model accuracy and computational efficiency, in particular, for patient-specific scenarios, remains a challenge. In this work, we present a continuum-based approach for simulating platelet plug formation using adaptive mesh refinement, providing a novel solution in this field that enables both accuracy and computational feasibility. Indeed, it integrates a stabilized finite element method within the Variational Multiscale framework to model blood flow dynamics, treated as a non-Newtonian fluid, along with the transport of biochemical species such as platelets and agonists. The platelet plug is represented by an extra stress term in the Navier–Stokes equation, capturing its influence on local blood flow dynamics as a rigid body. A key feature is related to anisotropic mesh adaptation, enabling high-resolution representation of the evolving platelet plug boundary while drastically reducing computational cost. We validate the model against two-dimensional benchmarks under varying shear rates and apply it to a 3D scenario, demonstrating its scalability and precision in simulating thrombosis under complex hemodynamic conditions. The results highlight the model's unique capability to facilitate accurate and efficient patient-specific simulations, offering a transformative tool for advancing personalized medicine.