A novel umbilical cord clamp and a combined umbilical cord clamp and cutter are provided for clamping and cutting umbilical cords in one motion. The cutter comprises two shells joined by a longitudinal hinge. A transverse blade is mounted in one shell, and a cutting support is mounted in the other shell across from the blade. One or more removable clamps may be engaged with the shells to be removable from the shells after cutting. Alternatively, a self-winding or plastically deformable band may be engageable with the shells. The cutter and its associated removable clamp(s) may be coordinated with an identifier, such as a color, number, or letter. Blood sampling and diagnostic features may be included with the cutter. The removable clamps may have an openable closure.