A tissue cutting device is disclosed, comprising a tubular part, that is structured and arranged to be inserted in a temporary delivery shape through a vascular system into a body vessel, and to be subsequently subjected to a change of shape, from said temporary delivery shape via an expanded delivered shape to a further expanded shape, extending at least beyond an outer surface of said body vessel in order to create a cutting action configured for cutting said body vessel, wherein said tissue cutting device is structured and arranged to penetrate a wall of said body vessel by said cutting action, in such a manner that a cut of said tissue created by said cutting action is continuously replaced by scar tissue, wherein the tubular part of said device comprises a plurality of segments connected to each other in longitudinal direction of said tubular part of said device, wherein a first segment of said plurality of segments has a dimension in a direction perpendicular to said longitudinal direction of said tubular part of said device that is larger than that dimension of a second segment thereof, at least in said expanded delivered shape.