A device for cutting tissue at a targeted cardiac valve, the device comprising: a catheter having a proximal end and a distal end, the distal end of the catheter being positionable at the targeted cardiac valve; a cutting mechanism positionable at the distal end of the catheter, the cutting mechanism including one or more cutting elements configured to cut leaflet tissue of the targeted cardiac valve when engaged against the leaflet tissue, wherein each of the one or more cutting elements are configured as a blade structure or a needle structure, and wherein the cutting mechanism is translatable within the catheter such that it is routable through the catheter to be passed beyond the distal end of the catheter and/or to be retracted proximally into the catheter; a handle coupled to the proximal end of the catheter, the handle including an electrical source for powering oscillating motion of the one or more cutting elements; a stabilizing assembly extendable distally past the distal end of the catheter, the stabilizing assembly being configured to engage against the targeted cardiac valve to stabilize the distal end of the catheter relative to the targeted valve, wherein the stabilizing assembly includes a cup; and wherein the cup is attached to an inner member which extends proximally from the cup toward the handle, wherein the inner member is configured to be advanced or retracted relative to the catheter to advance the cup past the distal end of the catheter or to retract the cup into the catheter, respectively, the cup being configured to engage with the leaflet tissue and to receive cut leaflet tissue and/or an interventional device implanted into the cut leaflet tissue, the cup including one or more pivot points that allow the cup to collapse into a more oblong and lower profile shape as a peripheral curvature of the cup is forced against the distal end of the catheter. a catheter having a proximal end and a distal end, the distal end of the catheter being positionable at the targeted cardiac valve; a cutting mechanism positionable at the distal end of the catheter, the cutting mechanism including one or more cutting elements configured to cut leaflet tissue of the targeted cardiac valve when engaged against the leaflet tissue, wherein each of the one or more cutting elements are configured as a blade structure or a needle structure, and wherein the cutting mechanism is translatable within the catheter such that it is routable through the catheter to be passed beyond the distal end of the catheter and/or to be retracted proximally into the catheter; a handle coupled to the proximal end of the catheter, the handle including an electrical source for powering oscillating motion of the one or more cutting elements; a stabilizing assembly extendable distally past the distal end of the catheter, the stabilizing assembly being configured to engage against the targeted cardiac valve to stabilize the distal end of the catheter relative to the targeted valve, wherein the stabilizing assembly includes a cup; and wherein the cup is attached to an inner member which extends proximally from the cup toward the handle, wherein the inner member is configured to be advanced or retracted relative to the catheter to advance the cup past the distal end of the catheter or to retract the cup into the catheter, respectively, the cup being configured to engage with the leaflet tissue and to receive cut leaflet tissue and/or an interventional device implanted into the cut leaflet tissue, the cup including one or more pivot points that allow the cup to collapse into a more oblong and lower profile shape as a peripheral curvature of the cup is forced against the distal end of the catheter.