As high-performance computing shifts toward GPU-accelerated exascale systems, the exponential growth of scientific data poses severe challenges to both storage capacity and I/O bandwidth. While current GPU-based lossy compressors attempt to address this by porting CPU algorithms to the device, they rely heavily on block-wise spatial decomposition to fit GPU parallelism. This approach suffers from a fundamental locality barrier: by partitioning data into independent blocks, these methods fail to capture global correlations and fragment the unified data patterns required for effective coding, severely limiting compression ratios. In this paper, we propose TZ, a novel GPU-native error-bounded lossy compressor that breaks this ceiling by adopting global Tucker decomposition. By prioritizing global spectral energy compaction over local approximation, TZ naturally maximizes the compression potential for scientific datasets. To render this computationally intensive approach practical for high-throughput GPU workflows, we introduce a highly optimized adaptive randomized SVD engine. This design allows TZ to achieve the superior compression ratios of global spectral decomposition while maintaining competitive execution speeds. Furthermore, the global processing nature of TZ enables a unified quantization and coding scheme that eliminates block artifacts and metadata overhead. Evaluation on production-scale scientific datasets demonstrates that TZ achieves approximately 10 × higher compression ratios than state-of-the-art GPU compressors under the same error bound, while maintaining competitive, high-throughput performance.