A method for automatically fixing sutures to secure a valve sleeve including an annular cuff and a replacement heart valve to an annulus formed in a patient's heart, includes the steps of removing an existing heart valve thereby forming an annulus in the patient's heart, and placing a first cylinder having a first end and a second end and an interior surface and an exterior surface and comprising first securing means formed on the exterior surface adjacent to the second end of the first cylinder, in which the first cylinder includes a valve sleeve having an annular cuff, such that the annular cuff surrounds the exterior surface adjacent to the first end of the first cylinder. Moreover, the method includes creating a blood-tight seal between the cuff of the valve sleeve and the annulus, and securing the plurality of sutures between the first cylinder and the second cylinder.