Light aircraft Flight Instructor reported an NMAC with another light aircraft while on short final to CMD airport. Flight executed an emergency breakaway and returned for landing.

Narrative

I was the Pilot in Command (PIC) of Aircraft X; conducting flight instruction with a student pilot on board. We were established on a stabilized short final for Runway 02 at CMD. I was actively monitoring CTAF and made at least three clear position reports on the final approach leg.During the approach; an aircraft in the pattern made two urgent radio calls advising of 'two aircraft in close proximity' on final. I verbally acknowledged the pilot's call. However; because I was the only aircraft making position reports on final and was managing spacing for the plane clearing the runway ahead; I reasonably concluded the warning referred to my distance from the ground traffic.At approximately 200 ft AGL; Aircraft Y overtook my aircraft from a blind spot above and behind. Aircraft Y had failed to announce its position or pattern entry since its previous call at high altitude. The aircraft dropped directly into my flight path within an estimated 20-30 feet of operation off my nose to the left and at a high rate of speed.To avoid an immediate collision and turbine wake at a critically low altitude; I initiated an emergency go-around. Almost simultaneously; Aircraft Y called a go-around. Because the aircraft was directly in front/below me and powering up; I executed an immediate emergency breakaway maneuver; banking right and to the east to exit the traffic area to avoid a second collision and maintain visual separation.