The sharpest substance would lead to the sharpest knife. Currently Obsidian is considered to be the sharpest blade you can get. The thinnest blades known are three nanometers wide at the edge. The knife is said to be ten times sharper than the edge of a razor blade.
Obsidian is actually a stone formed by volcanic activity. The material is also called volcanic glass due to it’s looks. The Obsidian blades are constructed by flaking a long and thin sliver from the core of an Obsidian stone.
They do make very fine surgical knives given their edge and sharpness, however since they have a tendency to break easily, they are not yet used for human surgeries. It would be disastrous if the scalpel being used for the surgery were to break midway and embed glass into the patient.
The glass fragments would complicate an already dicey surgery. This is why despite being the sharpest material in the world, Obsidian knives are not licensed for use during human surgeries. Most surgical knives are usually made of metal which is much more sturdy.
Make a science project out of finding out what other materials are hard and sharp. Make different lists for materials that are found in nature and those which are man made.