PROBLEM TO BE SOLVED: To provide a cutting device and a cutting method for cutting a glass rod having a large diameter without breaking the glass rod to device and a cutting method of the glass rod, for cutting the glass rod having a large diameter without breaking glass rod to provide a smooth cutting surface. SOLUTION: A glass rod 1 is cut by rotating a cutting blade 2 having the blade at the outer periphery of a disk, and moving the rotating cutting blade into the glass rod 1. Especially, when the glass rod is cut in a state, in which the longitudinal direction of the glass rod is fixed in the perpendicular direction, the glass rod is supported by applying the reaction against the force applied to the glass rod by the cutting blade 2 to the glass rod so that the direction of the reaction may be in the reverse direction of the moving direction of the cutting blade 2 when the cut is carried out in the horizontal direction, and the glass rod is supported at the position near to the moving position of the cutting blade to the extent that the glass rod is allowed to be cut when the glass rod is cut in the perpendicular direction, and fixing the glass rod at the position far from the positions for supporting the glass rod in the perpendicular direction.