Systolic Anterior Motion (SAM) of the mitral valve - often associated with Hypertrophic Obstructive Cardiomyopathy (HOCM) - is a cardiac pathology in which a functional subaortic stenosis is induced during systole by the mitral leaflets partially obstructing the outflow tract of the left ventricle. Its assessment by diagnostic tests is often difficult, possibly underestimating its severity and thus increasing the risk of heart failure. In this paper, we propose a new computational pipeline, based on cardiac cine Magnetic Resonance Imaging (cine-MRI) data, for the assessment of SAM. The pipeline encompasses image processing of the left ventricle and the mitral valve, and numerical investigation of cardiac hemodynamics by means of Computational Fluid Dynamics (CFD) in a moving domain with image-based prescribed displacement. Patient-specific geometry and motion of the left ventricle are considered in view of an Arbitrary Lagrangian-Eulerian approach for CFD, while the reconstructed mitral valve is immersed in the computational domain by means of a resistive method. We assess clinically relevant flow and pressure indicators in a parametric study for different degrees of SAM severity, in order to provide a better quantitative evaluation of the pathological condition. Moreover, we provide specific indications for its possible surgical treatment, i.e. septal myectomy.