Artificial intelligence (AI) empowered edge computing has given rise to a new paradigm and effectively facilitated the promotion and development of multimedia applications. The speech assistant is one of the significant services provided by multimedia applications, which aims to offer intelligent interactive experiences between humans and machines. However, malicious attackers may exploit spoofed speeches to deceive speech assistants, posing great challenges to the security of multimedia applications. The limited resources of multimedia terminal devices hinder their ability to effectively load speech spoofing detection models. Furthermore, processing and analyzing speech in the cloud can result in poor real-time performance and potential privacy risks. Existing speech spoofing detection methods rely heavily on annotated data and exhibit poor generalization capabilities for unseen spoofed speeches. To address these challenges, this paper first proposes the Coordinate Attention Network (CA2Net) that consists of coordinate attention blocks and Res2Net blocks. CA2Net can simultaneously extract temporal and spectral speech feature information and represent multi-scale speech features at a granularity level. Besides, a contrastive learning-based speech spoofing detection framework named GEMINI is proposed. GEMINI can be effectively deployed on edge nodes and autonomously learn speech features with strong generalization capabilities. GEMINI first performs data augmentation on speech signals and extracts conventional acoustic features to enhance the feature robustness. Subsequently, GEMINI utilizes the proposed CA2Net to further explore the discriminative speech features. Then, a tensor-based multi-attention comparison model is employed to maximize the consistency between speech contexts. GEMINI continuously updates CA2Net with contrastive learning, which enables CA2Net to effectively represent speech signals and accurately detect spoofed speeches. Extensive experiments on the ASVspoof2019 dataset show that GEMINI reduces the Equal Error Rate and tandem Detection Cost Function by up to 96.75% and 96.35% in the physical access scenario, and by up to 86.62% and 87.71% in the logical access scenario compared to peer methods.