This device for cutting off and removing calcified tissue from a heart valve, comprises a tubular body (1) suitable for being inserted by minimally invasive or endoscopic channel in relation with a previously inserted wire guide (g) suitable for passing through the flaps of the valve above the part where the calcified tissue needs to be removed, one of the ends of said body (1), viewed at said flaps, having a profiled end piece (2) made from flexible material and arrangements (1a) for a lateral projection of a cutting member (3) for cutting said tissue, the end of the body (1) having, upstream from the arrangements (1a) for the lateral projection of the cutting member (3), a laterally offset rounded area (1b) delimiting, on the same side as the arrangement (1a), a hollow portion (1b1), and on the opposite side, a projecting portion (1b2) suitable for bearing on the flaps during the cutting operation under the effect of a rotational movement of the body (1) that can be actuated by a single hand from a handle (4) located on the outside in order to decalcify the whole valve, said arrangement (1a) being in communication with means (6) for sucking up the cut-off tissue.