A system for manufacturing a three-dimensional object facilitates the removal of support material from the object. The system includes a controller configured to move a platen to position the object at a position opposite a microwave radiator and then operate the microwave radiator to change the phase of the support material from solid to liquid. The controller either monitors the expiration of a predetermined time period or a temperature of the object to determine when the microwave radiator operation is terminated. The microwave radiation does not damage the object because the support material has a dielectric loss factor that is greater than the dielectric loss factor of the object.