The invention discloses a pipe clamping device and a pipe cutting machine. The pipe clamping device comprises a base frame, a first clamping structure, a second clamping structure, a telescopic mechanism and a supporting and fixing mechanism, and a long-strip pipe to be machined is placed between the first clamping structure and the second clamping structure; the first clamping structure and the second clamping structure can abut against the inner side edges of the two ends of the pipe correspondingly, so that the pipe is clamped and fixed, the telescopic mechanism drives the supporting and fixing mechanism to move and stretch into the pipe, and the supporting and fixing mechanism abuts against the inner wall of the pipe so that supporting and bearing can be provided for the middle position of the pipe; therefore, shaking of the pipe is reduced, more stable clamping of the whole to-be-machined pipe is achieved, the cutting machining precision is guaranteed, the first clamping structure, the second clamping structure and the supporting and fixing mechanism all act on the inner side of the pipe, the pipe clamping and supporting occupy few pipe positions, the appearance of the pipe can be prevented from being damaged, tailings can be reduced, and the cost is saved.