While you could cut directly on some stone countertops, however it is not recommended.
Granite is known to be one of the most durable countertop materials you can purchase, and it can without doubt withstand cuts from a knife blade. However, if your granite has a sealer, cutting on it can eventually wear down the sealant. Over time, this can lead to liquids and food being absorbed by the stone, which could cause stains and other issues that require repair.
When using unsealed granite, cutting may be less of an issue, though again not recommended. Generally the stone is hard enough to cut on without it scratching, however doing so can lead to dulling of your knife blades rather quickly.
Similarly, quartz is an extremely durable, scratch resistant countertop which in most cases can be cut on without damaging the stone. Although, Quartz is not completely scratch proof, therefore it is still possible to cause some damage.
Other natural stones are often softer and are more likely to scratch if a knife is used on the surface. Limestone, marble, and sandstone are among these. Most of these stones also require a sealer, which again can be damaged and lead to stains and scratches. Soapstone is a lot softer stone that scratches quite easily, however it could be restored by standing or rubbing mineral oil.
While it is possible to cut directly on top of natural stone, it’s generally easier and safer in the long run to use a cutting board.
For professional assistance on proper natural stone care, feel free to contact Turkish Marble Company