A method and a device for cutting off a substrate of fragile material which can prevent the substrate of fragile material from being damaged or contaminated through contact by preventing contact of divided surfaces in a break process for cutting off the substrate of fragile material continuously. The device for cutting off a substrate of fragile material comprises dividing means (112, 122) for exerting a pressing force to the vicinity of a scribe line S formed on a substrate G and cutting off the substrate G at the pressed portion, and a holding portion moving substantially in parallel with the scribe line S while holding the dividing means to cut off the substrate G continuously along the scribe line S. The holding portion is provided with divided surface separating means (113, 123) for pressing at least one part of the divided substrate G while clamping it, and moving the substrate G substantially in parallel with the major surface thereof and in such a direction that the opposing divided surfaces obtained by cutting off separate from each other.