When the tension er come off on a2001 Mazda Etude 1600e what can the damage to the engine be

If you are talking about the serpentine belt tensioner , not such a big deal as long as you don't over heat the engine due to no water pump. If you are talking about the timing belt tensioner , it could be big trouble. I am not familiar with your engine , but if it is an interference engine , serious damage would be done by the pistons hitting the valves. I will keep my fingers crossed that your car has a non-interference engine.

Is this the fan (serpentine accessory) belt, or the cam belt? the fan belt drives the alternator, air conditioner, etc, and is visible on the front of the engine. The cam belt is usually behind a cover of some kind and can't be seen.
If it is the fan belt, no damage. If it is the cam belt, it depends on the engine design. maybe no damage, maybe serious damage to the valves. If you replaced the tensioner and properly aligned the cam and crank pulleys, and it won't start, you most likely have serious damage to the valves. You will need to pull the head, have the damaged valves replaced, after inspecting the pistons for damage.