I stand corrected. You are correct that some veins do become varicose following circumcision. However the cutting of larger veins is avoided whenever possible. Here is the technique:
Circumcision is performed with the penis retracted. Grasp the prolapsed portion of the prepuce with grasping forceps positioned 180° from each other. Elongate the prepuce and hold it open by retracting the grasping forceps away from the bull and each other. Insert two fingers of one hand into the preputial cavity with the palm facing up. Flex the fingers to apply additional tension to half of the prepuce so that any large vessels laying between the internal and external epithelial layers are identified. Make a liner incision, parallel to the long axis of the prepuce and measuring 2-3 cm in length, through the external epithelial layer beginning 2-3 cmproximal to the damaged portion of the prepuce and proceeding distally. Take care to avoid large vessels in the area. Extend the incision through the elastic lamina of the prepuce and the internal epithelial layer until the preputial cavity is entered. Vessels encountered while incisingthrough the preputial layers should be double ligated and transected between the ligatures. Grasp the external lamina of the preputial epithelium with thumb forceps and rotate it in such a way that any large vessels located in the elastic lamina on either side of the linear incisions can be identified, ligated and transected. Suture the internal epithelial laminae of the prepuce to the external epithilial laminae along each side of the incision, beginning at the proximal aspect and proceeding distally, for approximately 1-2 cm. Beginning on one side of the linearincision, make a circumfrential incision perpendicular to long axis of the prepuce and extend itjust through the external epithelial laminae, at the point where the internal and external epithelial lamina are unopposed. Extend the circumfrential incision 3-5 cm and gradually deepen it to expose vessels laying in the elastic laminae of the prepuce. Ligate and transect large vessels as previously described. Increase the depth of the incision until all the elastic laminae and the internal epithelial lamina have been incised. Suture the internal epithelial laminae to the external epithelial laminae. Lengthen the circumfrential incision in increments of 3-5 cm until the entire circumference of the prepuce has been incised and the proximaledges of the internal and external epithelial laminae are sutured together.