A system is disclosed for use in additively manufacturing a composite structure. The system may include a head having a nozzle configured to discharge a composite material, including a matrix and a continuous reinforcement. The system may also include a cure enhancer configured to enhance curing of the matrix, and a support configured to move the head during discharging to create a structure having a three-dimensional trajectory. The system may further include a cutting mechanism operatively mounted to at least one of the head and the support, and configured to sever the continuous reinforcement after discharge from the nozzle. The cutting mechanism may include a blade, and an ultrasonic energy source connected to the blade.