Large language models (LLMs) have demonstrated their effectiveness in multivariate time series classification (MTSC). Effective adaptation of LLMs for MTSC necessitates informative data representations. Existing LLM-based methods directly encode embeddings for time series within the latent space of LLMs from scratch to align with semantic space of LLMs. Despite their effectiveness, we reveal that these methods conceal three inherent bottlenecks: (1) they struggle to encode temporal and channel-specific information in a lossless manner, both of which are critical components of multivariate time series; (2) it is much difficult to align the learned representation space with the semantic space of the LLMs; (3) they require task-specific retraining, which is both computationally expensive and labor-intensive. To bridge these gaps, we propose TableTime, which reformulates MTSC as a table understanding task. Specifically, TableTime introduces the following strategies: (1) convert multivariate time series into a tabular form, thus minimizing information loss to the greatest extent; (2) represent tabular time series in text format to achieve natural alignment with the semantic space of LLMs; (3) design a reasoning framework that integrates contextual text information, neighborhood assistance, multi-path inference and problem decomposition to enhance the reasoning ability of LLMs and realize zero-shot classification. Extensive experiments performed on 10 publicly representative datasets from UEA archive verify the superiorities of the TableTime.