A device for cutting off and removing calcified tissue from a heart valve, including a tubular body suitable for being inserted by way of a minimally invasive or endoscopic channel in relation to a previously inserted guide wire suitable for passing through the flaps of the valve above the portion where the calcified tissue is to be removed. One of the ends of the body, viewed at the flaps, has a profiled tip made of flexible material and arrangements for the lateral projection of a cutting member for cutting the tissue. The end of the body has, upstream from the arrangements for the lateral projection of the cutting member, a laterally offset rounded area defining, on the same side as the arrangements, a recessed portion and, on the opposite side, a projecting portion suitable for bearing upon the flaps during the cutting procedure under the effect of a rotational movement of the body that can be actuated using only one hand by way of a handle located externally in order to decalcify the whole valve. The arrangements are in communication with a mechanism for sucking away the cut tissue.