We propose a framework for odometry, mapping and ground segmentation using a backpack LiDAR system that achieves both real-time and low-drift performance. First, we present a spatio-temporal calibration method to carefully merge scans from the two laser scanners on a backpack. Second, we propose a feature extraction method which generalizes a point's geometrical characteristics as two groups (disjoint, continuous) and three types (edge, corner, plane). The extracted features are used in point cloud registration in the odometry and mapping tasks. Third, a fast ground segmentation method is customized for the backpack LiDAR system. Finally, we evaluate the proposed method in four datasets logged by the backpack across different scales and environments. Furthermore, NTU VIRAL dataset is used to benchmark our method quantitatively. Experiments show that our method consistently outperforms the state-of-the-art methods before using loop closure optimization and sensor fusion techniques.