Moving object segmentation is critical to interpret scene dynamics for robotic navigation systems in challenging environments. Neuromorphic vision sensors are tailored for motion perception due to their asynchronous nature, high temporal resolution, and reduced power consumption. However, their unconventional output requires novel perception paradigms to leverage their spatially sparse and temporally dense nature. In this work, we propose a novel event-based motion segmentation algorithm using a Graph Transformer Neural Network, dubbed GTNN. Our proposed algorithm processes event streams as 3D graphs by a series of nonlinear transformations to unveil local and global spatiotemporal correlations between events. Based on these correlations, events belonging to moving objects are segmented from the background without prior knowledge of the dynamic scene geometry. The algorithm is trained on publicly available datasets including MOD, EV-IMO, and \textcolor{black}{EV-IMO2} using the proposed training scheme to facilitate efficient training on extensive datasets. Moreover, we introduce the Dynamic Object Mask-aware Event Labeling (DOMEL) approach for generating approximate ground-truth labels for event-based motion segmentation datasets. We use DOMEL to label our own recorded Event dataset for Motion Segmentation (EMS-DOMEL), which we release to the public for further research and benchmarking. Rigorous experiments are conducted on several unseen publicly-available datasets where the results revealed that GTNN outperforms state-of-the-art methods in the presence of dynamic background variations, motion patterns, and multiple dynamic objects with varying sizes and velocities. GTNN achieves significant performance gains with an average increase of 9.4% and 4.5% in terms of motion segmentation accuracy (IoU%) and detection rate (DR%), respectively.