Anomaly segmentation has been widely applied to diagnosis of medical organs and lesions and detection of industrial defects. However, existing methods still face challenges in extracting discriminant image features and utilizing semantic information. To address these issues, we propose a Text-Prompted Dual-Path Convolution-Mamba Network (TPCM-SegNet)\footnote{The code and models will be available at https://indtlab.github.io/projects/TPCM-SegNet upon the acceptance of the paper.}, which integrates Residual Double-Convolution Blocks (RDCBs) and Mamba-Transformer Blocks (MTBs) in two parallel paths for the purpose of extracting local and global features, respectively. Given a pair of RDCB and MTB at the same stage, a Feature Fusion Block (FFB) is introduced in order to facilitate the interaction and fusion of the features extracted using these blocks. Furthermore, we fuse the text tokens extracted from a textual description with the image features extracted using each of those blocks through a Text Prompt Block (TPB), to enhance the semantics understanding ability of the network. A Cascade Feature Block (CFB) is also designed for each stage of the encoder, to combine the feature maps, the logit maps decoded from them and the input image. This block incorporates the prior and original characteristics into the image representation. Experimental results demonstrate that our TPCM-SegNet achieves the superior, or at least comparable, performance to baselines, across eight publicly available datasets. These promising results should benefit from the powerful ability of image representation and semantic understanding of the proposed network.