The relief angle is the angle between a cutting tool and the workpiece it has just cut. The relief angle on a machine tool is the angle that the edge of the tool nearest the workpiece makes with the workpiece. If the relief angle is too small the side of the tool will not clear the work and will rub.

the cutting edge (of sth) the most recent and advanced stage of development in a particular type of work or activity, with the newest systems, equipment, etc.: We want to be at the cutting edge of this technology.

The phrase "cutting-edge approach" is correct and usable in written English. You can use it whenever you are referring to something that is highly advanced or ahead of its time - for example, "The new project uses a cutting-edge approach to solve an age-old problem."

The adjective cutting-edge often describes new advances in science or technology — a hospital might advertise its use of cutting-edge cancer treatments, for example. Art can be described as cutting-edge as well, if it uses innovative techniques or does something completely new.