A laser pipe cutting device is provided. It includes a cutting head, a lathe bed, a first chuck, a second chuck and a third chuck; the first chuck is a fixed chuck for positioning axially and radially a pipe fitting; the second chuck is a rolling chuck for positioning radially the pipe fitting; and a fixed clamping disc and a rolling clamping disc are arranged on the third chuck at both ends. In the scheme, the third chuck integrates both the rolling clamping function and the fixed clamping function to achieve larger supporting weight and more accurate clamping precision, so that the chucks can drive a thin pipe fitting to rotate at a higher speed, the cutting efficiency is improved, and no-dead-angle and zero-tailing cutting is achieved.