Evolutionary computing, particularly genetic algorithm (GA), is a combinatorial optimization method inspired by natural selection and the transmission of genetic information, which is widely used to identify optimal solutions to complex problems through simulated programming and iteration. Due to its strong adaptability, flexibility, and robustness, GA has shown significant performance and potentiality on perturbed substructure optimization (PSSO), an important graph mining problem that achieves its goals by modifying network structures. However, the efficiency and practicality of GA-based PSSO face enormous challenges due to the complexity and diversity of application scenarios. While some research has explored acceleration frameworks in evolutionary computing, their performance on PSSO remains limited due to a lack of scenario generalizability. Based on these, this paper is the first to present the GA-based PSSO Acceleration framework (GAPA), which simplifies the GA development process and supports distributed acceleration. Specifically, it reconstructs the genetic operation and designs a development framework for efficient parallel acceleration. Meanwhile, GAPA includes an extensible library that optimizes and accelerates 10 PSSO algorithms, covering 4 crucial tasks for graph mining. Comprehensive experiments on 18 datasets across 4 tasks and 10 algorithms effectively demonstrate the superiority of GAPA, achieving an average of 4x the acceleration of Evox. The repository is in https://github.com/NetAlsGroup/GAPA.