The shedding of thrombosis can pose diagnostic difficulties for clinicians as it results in risks of damage. Determining the appropriate treatment, drug thrombolysis, implanted vascular stents, clinical research, or surgical cutting is often challenging. To better understand the interfacial mechanical mechanism of thrombus shedding, a fluid-solid coupling finite element model was created based on viscoelasticity-based blood vessels, line elastic thrombosis, and Euler fluid blood to establish a connective interface between blood vessels and thrombosis. Under hypertension conditions, the interface mechanics model calculated the finite element interface performance of thrombosis with different degrees of calcification, thicknesses, and coverage angles, using the mechanical parameters to assess damage for the interface of different structural thromboses. The study analyzed and clarified the evolution mechanism of damage and exfoliation of the thrombotic interface in blood vessels under various conditions. The results revealed that the mechanics of damage and the shedding mechanism of the thrombosis were significantly affected by the different coverage angles. Based on these analyses, this study determined that the finite element method based on the Coupled Eulerian–Lagrangian method, including the interface model of the cohesive zone volume element layer, could well simulate the mechanics of damage and the shedding mechanism of the thrombotic interface under the impact of hypertension. This study is the first to explore the finite element interface damage model of thrombosis and the vessel wall using interfacial mechanics.