A widely used treatment method for regurgitation in the mitral valve (MV) is by using an MV clip. This is a minimally invasive procedure, providing an alternative to higher risk open heart surgery. However, there are always uncertainties in the outcomes of the procedure, e.g. in how successfully the regurgitation is treated without causing significant stenosis of the valve. Thus, access to patient-specific simulations of the procedure could be a valuable tool for heart surgeons in treatment planning. Here we present a framework for such simulations, applying fluid-structure interaction (FSI) to si\-mu\-late the motion of the MV leaflets. The FSI approach is based on methods that we have previously used to simulate an idealized aortic valve. The mesh is monolithic, with the fluid interior and solid leaflets marked as separate subdomains in a single mesh. An arbitrary Lagrangian-Eulerian finite element method is used to handle the displacement of the leaflets and the heart wall motion. The mesh vertices of the solid parts follow the movement in a Lagrangian sense, with mesh smoothing algorithms to handle the mesh deformation, while the fluid is simulated in an Eulerian framework that also compensates for the displacement of the vertices. Contact between the leaflets is handled by marking a contact subdomain of the mesh between the leaflet tips. When the distance between the leaflet tips is below a certain threshold, the contact region switches state from fluid to solid, thus sealing off the opening. This allows for computation without the need for remeshing during runtime. Results from simulations done in our left ventricle model, with a planar model of the MV corresponding to a projection of the leaflets onto the valve opening, show that the mechanical stresses in the blood flow are higher after treatment with an MV clip. Moreover, the results also indicate that the placement of the clip is important in determining the outcome, and that results differ depending on if the clip is closer to the lateral or medial commissure. This model included neither the left atrium nor the valve leaflets, but through collaboration with clinics we will add these parts to the model, as well as the FSI approach, and be able to compare the results.