Blockchain data mining has the potential to reveal the operational status and behavioral patterns of anonymous participants in blockchain systems, thus providing valuable insights into system operation and participant behavior. However, traditional blockchain analysis methods suffer from the problems of being unable to handle the data due to its large volume and complex structure. With powerful computing and analysis capabilities, graph learning can solve the current problems through handling each node's features and linkage relationships separately and exploring the implicit properties of data from a graph perspective. This paper systematically reviews the blockchain data mining tasks based on graph learning approaches. First, we investigate the blockchain data acquisition method, integrate the currently available data analysis tools, and divide the sampling method into rule-based and cluster-based techniques. Second, we classify the graph construction into transaction-based blockchain and account-based methods, and comprehensively analyze the existing blockchain feature extraction methods. Third, we compare the existing graph learning algorithms on blockchain and classify them into traditional machine learning-based, graph representation-based, and graph deep learning-based methods. Finally, we propose future research directions and open issues which are promising to address.