Surging debris flows are among the most destructive natural hazards, and elucidating the interaction between coarse-grained fronts and the trailing liquefied slurry is key to understanding these flows. Here, we describe the application of high-resolution and high-frequency 3D LiDAR data to explore the dynamics of a debris flow at Illgraben, Switzerland. The LiDAR measurements facilitate automated detection of features on the flow surface, and construction of the 3D flow depth and velocity fields through time. Measured surface velocities (2-3 m s^-1) are faster than front velocities (0.8-2 m s^-1), illustrating the mechanism whereby the flow front is maintained along the channel. Further, we interpret the relative velocity of different particles to infer that the vertical velocity profile varies between plug flow and one that features internal shear. Our measurements provide unique insights into debris-flow motion, and provide the foundation for a more detailed understanding of these hazardous events.