Although Bitcoin has demonstrated its utility as a prominent cryptocurrency and a medium of economic exchange, its inherent pseudonymity—which preserves user anonymity—has contributed to a surge in illicit use, including money laundering and other illegal transactions. In particular, mixing services such as CoinJoin intentionally obfuscate transaction paths to hinder tracing of fund sources and flows. Consequently, existing on-chain analysis and transaction-level tracking methods struggle to effectively detect mixing activity. Moreover, prior studies employing graph neural networks (GNNs) for mixing detection typically adopt a global classification approach that models the entire transaction network as a single graph, which limits their ability to capture the granular context of individual transactions. In this paper, we construct a dataset comprising both illicit and legitimate Bitcoin transactions and propose a Subgraph-based GNN approach that models the adjacent flow of each transaction as an independent Subgraph to improve mixing detection. Experimental results show that the proposed method achieves over 97% accuracy. In addition, GraphSAGE yields the best performance, achieving an F1-score of 98.5% for identifying Bitcoin mixing transactions in our dataset. The proposed subgraph-based mixing detection approach can be applied to cryptocurrency crime investigations, and is expected to be particularly applicable to Anti-Money Laundering (AML) systems and blockchain forensic analysis tools that require tracking continuous flows of criminal funds.