Multivariate time series (MTS) anomaly detection is essential for maintaining the reliability of industrial systems, yet real-world deployment is hindered by two critical challenges: training data contamination (noises and hidden anomalies) and inefficient model inference. Existing unsupervised methods assume clean training data, but contamination distorts learned patterns and degrades detection accuracy. Meanwhile, complex deep models often overfit to contamination and suffer from high latency, limiting practical use. To address these challenges, we propose CLEANet, a robust and efficient anomaly detection framework in contaminated multivariate time series. CLEANet introduces a Contamination-Resilient Training Framework (CRTF) that mitigates the impact of corrupted samples through an adaptive reconstruction weighting strategy combined with clustering-guided contrastive learning, thereby enhancing robustness. To further avoid overfitting on contaminated data and improve computational efficiency, we design a lightweight conjugate MLP that disentangles temporal and cross-feature dependencies. Across five public datasets, CLEANet achieves up to 73.04% higher F1 and 81.28% lower runtime compared with ten state-of-the-art baselines. Furthermore, integrating CRTF into three advanced models yields an average 5.35% F1 gain, confirming its strong generalizability.