As one of the most important components of urban space, the geometric and semantic properties of road trees are crucial for the assessment and upgrade of urban environments. Accurate positioning of individual trees is a critical procedure for this task; however, traditional manual methods require considerable personnel and material resources. By contrast, individual tree segmentation based on a vehicle-mounted mobile laser scanner (MLS) operating along urban streets can provide a feasible and efficient solution. Recent studies (especially those based on deep learning) on point cloud semantic segmentation and forest tree detection have achieved significant progress; however, they rarely perform instance recognition of urban trees. In addition, extracting individual urban trees from point clouds to balance accuracy and efficiency remains challenging. To this end, we propose an effective pipeline to segment individual trees from urban MLS data. The proposed approach encompasses two main steps: tree-point extraction and individual-tree segmentation. First, a patch-guided semi-supervised semantic segmentation network was designed to separate non-tree points from entire urban scene. The extracted tree points are further divided into instance-level trees using a three-stage segmentation network for the individual tree segmentation. Specifically, a tree-centroid prediction module is proposed to ensure the accurate localization of street trees, even with irregular positions, in complex urban environments. Subsequently, a special confidence-aware attention mechanism is developed to resolve challenging ambiguities from complementary perspectives. Finally, a dynamic shifting-based clustering algorithm is introduced to speed up the segmentation of each tree guided by the predicted centroid and directly transfer the IDs back to the point clouds. The proposed method is evaluated and validated on MLS point clouds collected in two urban areas, robustly producing accurate instance-level roadside trees. The instance-level segmentation results in average precision and recall of (96.62%, 96.17%) and (95.62%, 94.58%), respectively, on these two MLS point cloud datasets. Point-level segmentation also exhibits mean precision, recall, and weighted coverage exceeding 90%. We also verify that the proposed method could achieve a promising result on an airborne laser scanning point cloud dataset without retraining, thereby demonstrating a good generalization ability. To further verify the quality of the segmented tree instances, a reconstruction method is adopted to employ these independent street trees in trunk point cloud modeling. Our contribution may assist in developing intelligent urban green space planning and management.