Diamonds can cut glass because they are extremely hard and have a sharp edge. Diamonds rank at the top of the Mohs hardness scale, which is a measure of mineral hardness. With a rating of 10, diamonds are the hardest naturally occurring substance known to humans.

When a diamond is fashioned into a cutting tool, such as a diamond-tipped glass cutter, its edges remain incredibly sharp and can exert a concentrated force on the glass. Due to the hardness differential, the diamond is able to scratch and cleave the glass without being worn down itself. Glass, which ranks around 5.5 to 7 on the Mohs scale depending on its composition, is significantly softer than diamond. Therefore, when a diamond edge encounters the glass surface, it can easily displace the atoms in the glass lattice, essentially scoring and fracturing it along a precise line.

Moreover, diamonds have excellent fracture toughness, meaning they can withstand the stress of cutting without cracking or breaking. This property, combined with their exceptional hardness and the ability to maintain a sharp edge, makes diamonds effective cutting tools for not just glass, but also many other materials.