Can diamonds cut anything

As a practical matter, you wouldn't use a diamond to cut paper, or wood or metal: the edge of the finished stone is simply too small to be used in these applications. (Plus there are better tools more suitable for cutting these materials.)

However, one test of a diamond is to use it to cut glass. Effectively, however, this test will only mar the surface of the glass plate.

(In the hands of a glass-cutter, though, a glass cutting tool is used in combination with a series of measurements, exact application of the cutting tool and rubber mallet taps, which ultimately cuts the glass into the desired pieces.)

You could be curious about the hardness of diamond: it is the hardest mineral on earth.