A tissue cutter includes a housing, a blade, a pivot, and a blade spring. The housing is shaped so as to define a channel that has proximal and distal openings and a central longitudinal axis, and is shaped for slidable disposition therein of a hollow tubular element having a tapered distal portion. The blade which extends alongside the central longitudinal axis, and defines a sharp cutting surface that reaches a distal-most point of the blade and faces away from the central longitudinal axis. The pivot couples the blade to the housing such that the blade is rotatable with respect to the housing around a pivot point of the blade. The blade spring is arranged to apply a force to the blade that pushes a distal portion of the blade against the tapered distal portion of the hollow tubular element when the blade is positioned alongside the tapered distal portion.
