Point-based networks have been widely used in the semantic segmentation of point clouds owing to the powerful 3D convolution neural network (CNN) baseline. Most of the current methods resort to intermediate regular representations for reorganizing the structure of point clouds for 3D CNN networks, but they may neglect the inherent contextual information. In our work, we focus on capturing discriminative features with the interactive attention mechanism and propose a novel method consisting of the regional simplified dual attention network and global graph convolution network. Firstly, we cluster homogeneous points into superpoints and construct a superpoint graph to effectively reduce the computation complexity and greatly maintain spatial topological relations among superpoints. Secondly, we integrate cross-position attention and cross-channel attention into a single head attention module and design a novel interactive attention gating (IAG)-based multilayer perceptron (MLP) network (IAG–MLP), which is utilized for the expansion of the receptive field and augmentation of discriminative features in local embeddings. Afterwards, the combination of stacked IAG–MLP blocks and the global graph convolution network, called IAGC, is proposed to learn high-dimensional local features in superpoints and progressively update these local embeddings with the recurrent neural network (RNN) network. Our proposed framework is evaluated on three indoor open benchmarks, and the 6-fold cross-validation results of the S3DIS dataset show that the local IAG–MLP network brings about 1% and 6.1% improvement in overall accuracy (OA) and mean class intersection-over-union (mIoU), respectively, compared with the PointNet local network. Furthermore, our IAGC network outperforms other CNN-based approaches in the ScanNet V2 dataset by at least 7.9% in mIoU. The experimental results indicate that the proposed method can better capture contextual information and achieve competitive overall performance in the semantic segmentation task.