Underwater acoustic target recognition (UATR) is extremely challenging due to the complexity of ship-radiated noise and the variability of ocean environments. Although deep learning (DL) approaches have achieved promising results, most existing models implicitly assume that underwater acoustic data lie in a Euclidean space. This assumption, however, is unsuitable for the inherently complex topology of underwater acoustic signals, which exhibit non-stationary, non-Gaussian, and nonlinear characteristics. To overcome this limitation, this paper proposes the UATR-GTransformer, a non-Euclidean DL model that integrates Transformer architectures with graph neural networks (GNNs). The model comprises three key components: a Mel patchify block, a GTransformer block, and a classification head. The Mel patchify block partitions the Mel-spectrogram into overlapping patches, while the GTransformer block employs a Transformer Encoder to capture mutual information between split patches to generate Mel-graph embeddings. Subsequently, a GNN enhances these embeddings by modeling local neighborhood relationships, and a feed-forward network (FFN) further performs feature transformation. Experiments results based on two widely used benchmark datasets demonstrate that the UATR-GTransformer achieves performance competitive with state-of-the-art methods. In addition, interpretability analysis reveals that the proposed model effectively extracts rich frequency-domain information, highlighting its potential for applications in ocean engineering.