Pose estimation and human action recognition (HAR) are pivotal technologies spanning various domains. While the image-based pose estimation and HAR are widely admired for their superior performance, they lack in privacy protection and suboptimal performance in low-light and dark environments. This paper exploits the capabilities of millimeter-wave (mmWave) radar technology for human pose estimation by processing radar data with Graph Neural Network (GNN) architecture, coupled with the attention mechanism. Our goal is to capture the finer details of the radar point cloud to improve the pose estimation performance. To this end, we present a unique feature extraction technique that exploits the full potential of the GNN processing method for pose estimation. Our model mmGAT demonstrates remarkable performance on two publicly available benchmark mmWave datasets and establishes new state of the art results in most scenarios in terms of human pose estimation. Our approach achieves a noteworthy reduction of pose estimation mean per joint position error (MPJPE) by 35.6% and PA-MPJPE by 14.1% from the current state of the art benchmark within this domain.