A brittle material substrate cutting method and cutting apparatus are provided, which prevent cut faces of a brittle material substrate from contacting each other after the cutting in a break step of continuously cutting the brittle material substrate, so that a damage or contamination on the brittle material substrate due to the contact can be prevented. A brittle material substrate cutting apparatus includes: a cutting section ( 112, 122 ) for applying a pressing force in a vicinity of a scribe line S formed on a substrate G and cutting the pressed portion of the substrate G; and a holding section moving parallel to the scribe line S while holding the cutting section. The brittle material substrate cutting apparatus continuously cuts the substrate G along the scribe line S. The brittle material substrate cutting apparatus further includes: a cut-face separating section ( 113, 123 ), provided in the holding section, for holding and pressing at least one part of cut substrate portions of the substrate G, wherein the cut substrate portions are generated as a result of the cutting and they oppose each other, and moving cut faces of the cut substrate portions approximately parallel to a main face of the substrate G and in directions to separate the cut faces from each other.