I have heard that we can cut objects with laser and water , can't we do the same with air?
In a small way we do. Sand blasting an object can produce very detailed objects, given the technique and equipment used to do so.
It would have to be a strong and precise enough stream of air to cut through objects.
A laser cuts with intense heat(light).Water cuts with high speed x the density of molecules . Airs molecules are just too loosely packed the any damage.
People use a sand blaster to remove paint from things like trucks but that's about it