To clarify, a crescent kick moves in an anticlockwise direction, the same kick moving in a clockwise direction is refered to as an Axe kick.

I have realised this is wrong, what I meant was an axe kick goes in an outward direction a crescent kick] in an inward direction. As a natural consequence of this crescent kicks are more effective when used in a circular manner, whereas axe kicks normally go straight up and down. (thanks to MALTP for reminding me to mention this) The most common uses for axe kicks tend to be breaking the nose from above and forcing down someones guard. Crescent kicks apply a sideways force.

The crescent kicks application against a knife is a dubious one, however often people would immediately follow said kick with a spinning kick. It does have the advantage of being agressive action, most knife defense techniques assume the knife holder attacks first.

MALTP has also pointed out that being cut on the leg is better than being cut on the body (see sacrificial defense). However I would still not recommend this as a course of action. If the knife is missed it is entirely too easy for your opponent to stab you.