MitralClip is a novel minimally invasive procedure to treat mitral valve (MV) regurgitation. It consists in clipping the mitral leaflets together to close the regurgitant hole. A careful preoperative planning is necessary to select respondent patients and to determine the clipping sites. Although preliminary indications criteria are established, they lack prediction power with respect to complications and effectiveness of the therapy in specific patients. We propose an integrated framework for personalized simulation of MV function and apply it to simulate MitralClip procedure. A patient-specific dynamic model of the MV apparatus is computed automatically from 4D TEE images. A biomechanical model of the MV, constrained by the observed motion of the mitral annulus and papillary muscles, is employed to simulate valve closure and MitralClip intervention. The proposed integrated framework enables, for the first time, to quantitatively evaluate an MV finite-element model in-vivo, on eleven patients, and to predict the outcome of MitralClip intervention in one of these patients. The simulations are compared to ground truth and to postoperative images, resulting in promising accuracy (average point-to-mesh distance: 1.47 +/- 0.24 mm). Our framework may constitute a tool for MV therapy planning and patient management.