Accurate and efficient multivariate time series (MTS) analysis is increasingly critical for a wide range of intelligent applications. Within this realm, Transformers have emerged as the predominant architecture due to their strong ability to capture pairwise dependencies. However, Transformer-based models suffer from quadratic computational complexity and high memory overhead, limiting their scalability and practical deployment in long-term and large-scale MTS modeling. Recently, Mamba has emerged as a promising linear-time alternative with high expressiveness. Nevertheless, directly applying vanilla Mamba to MTS remains suboptimal due to three key limitations: (i) the lack of explicit cross-variate modeling, (ii) difficulty in disentangling the entangled intra-series temporal dynamics and inter-series interactions, and (iii) insufficient modeling of latent time-lag interaction effects. These issues constrain its effectiveness across diverse MTS tasks. To address these challenges, we propose DeMa, a dual-path delay-aware Mamba backbone. DeMa preserves Mamba's linear-complexity advantage while substantially improving its suitability for MTS settings. Specifically, DeMa introduces three key innovations: (i) it decomposes the MTS into intra-series temporal dynamics and inter-series interactions; (ii) it develops a temporal path with a Mamba-SSD module to capture long-range dynamics within each individual series, enabling series-independent, parallel computation; and (iii) it designs a variate path with a Mamba-DALA module that integrates delay-aware linear attention to model cross-variate dependencies. Extensive experiments on five representative tasks, long- and short-term forecasting, data imputation, anomaly detection, and series classification, demonstrate that DeMa achieves state-of-the-art performance while delivering remarkable computational efficiency.