A replacement mitral valve prosthesis includes a support structure and a valve body having three flexible leaflets. The support structure preferably includes an internal valve frame and an external sealing frame. The valve frame supports the flexible leaflets. The sealing frame is adapted to conform to the shape of the native mitral valve annulus. The sealing frame may be coupled to an inlet end of the valve frame, an outlet end of the valve frame, or both. A plurality of anchors is coupled to the outlet end of the valve frame. The anchors extend radially outwardly for placement behind native leaflets. The prosthesis preferably includes a skirt disposed along an exterior of the external sealing frame. The prosthesis is collapsible for delivery into the heart via a delivery catheter. The prosthesis is configured to self-expand for deployment in the heart when released from the delivery catheter.