Electroencephalography (EEG) signals are frequently contaminated by artifacts, affecting the accuracy of subsequent analysis. Traditional artifact removal methods are often computationally expensive and inefficient for real-time applications in edge devices. This paper presents a method to reduce the computational cost of most existing convolutional neural networks (CNN) by replacing one-dimensional (1-D) CNNs with two-dimensional (2-D) CNNs and deploys them on Edge Tensor Processing Unit (TPU), which is an open-resource hardware accelerator widely used in edge devices for low-latency, low-power operation. A new Efficient 2D-CNN Artifact Removal (E2CAR) framework is also represented using the method above, and it achieves a 90\% reduction in inference time on the TPU and decreases power consumption by 18.98\%, while maintaining comparable artifact removal performance to existing methods. This approach facilitates efficient EEG signal processing on edge devices.