The device is intended to be positioned in a sealed introducer arranged in the thoracic cavity between two ribs in order to penetrate into the left ventricle, passing through the apex of the heart. According to the invention, the device includes a body having a handle and at least one control member capable of acting on an assembly for installing and securing a braid to the mitral annulus by means of suturing elements, the assembly has a mechanism capable of enabling the extraction of a suture through the mitral valve while also being capable of enclosing the braid and becoming anchored to the periphery of the mitral annulus under the clamping effect of the suture, exerting two opposing pressure-bearing forces.