Mobile robots outfitted with a supportive tether are ideal for gaining access to extreme environments for mapping when human or remote observation is not possible. This paper is a field report covering both the development and field testing of our Tethered Robotic eXplorer (TReX) to map a steep, tree-covered rock outcrop in a gravel mine. TReX is a mobile robot designed for the purpose of mapping extremely steep and cluttered environments for geologic and infrastructure inspection. In comparison to other systems, our design improves tethered mobility by enabling rotational freedom on steep slopes using a center-pivoting tether management payload. To map the terrain, we leverage the rotation of an actuated tether spool with an attached two-dimensional (2D) lidar, which rotates to both manage tether and produce 3D scans. Given that mapping requires vehicle motion, we also evaluate two existing, real-time approaches to estimate the trajectory of the robot and rectify motion distortion from individual scans before alignment into the map: (a) a continuous-time, lidar-only approach that handles asynchronous measurements using a physically motivated, constant-velocity motion prior, and (b) a method that computes visual odometry from streaming stereo images to use as a motion estimate during scan collection. Once rectified, individual scans are matched to the global map by an efficient variant of the Iterative Closest Point (ICP) algorithm. Our results include a comparison of estimated maps and trajectories to ground truth (measured by a remote survey station), an example of mapping in highly cluttered terrain, and lessons learned from the design and deployment of TReX.