Unsupervised graph-level anomaly detection (UGLAD) is a critical and challenging task across various domains, such as social network analysis, anti-cancer drug discovery, and toxic molecule identification. However, existing methods often struggle to capture long-range dependencies efficiently and neglect the spectral information. Recently, selective state space models, particularly Mamba, have demonstrated remarkable advantages in capturing long-range dependencies with linear complexity and a selection mechanism. Motivated by their success across various domains, we propose GLADMamba, a novel framework that adapts the selective state space model into UGLAD field. We design a View-Fused Mamba (VFM) module with a Mamba-Transformer-style architecture to efficiently fuse information from different graph views with a selective state mechanism. We also design a Spectrum-Guided Mamba (SGM) module with a Mamba-Transformer-style architecture to leverage the Rayleigh quotient to guide the embedding refinement process, considering the spectral information for UGLAD. GLADMamba can dynamically focus on anomaly-related information while discarding irrelevant information for anomaly detection. To the best of our knowledge, this is the first work to introduce Mamba and explicit spectral information to UGLAD. Extensive experiments on 12 real-world datasets demonstrate that GLADMamba outperforms existing state-of-the-art methods, achieving superior performance in UGLAD. The code is available at https://github.com/Yali-Fu/GLADMamba .