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Adversarial attack plays a critical role in evaluating the robustness of deep learning models. Jacobian-based Saliency Map Attack (JSMA) is an interpretable adversarial method that offers excellent pixel-level control and provides valuable insights into model vulnerabilities. However, its quadratic computational complexity O(M^2 xN) renders it impractical for large-scale datasets, limiting its application despite its inherent value. This paper proposes FastJSMA, an efficient attack method that addresses these computational limitations. Our approach introduces a gradient decoupling mechanism that decomposes the Jacobian calculation into complementary class suppression (g^-) and class excitation (g^+) gradients, reducing complexity to O(M\sqrt N ). Additionally, we implement a class probing mechanism and an adaptive saliency threshold to further optimize the process. Experimental results across multiple datasets demonstrate that FastJSMA maintains comparable attack success rates while dramatically reducing computation time--requiring only 2.9% of JSMA's processing time on CIFAR-10 and 1.2% on CIFAR-100, and successfully operating on ImageNet where traditional JSMA fails due to memory constraints. This advancement enables the practical application of interpretable saliency map-based attacks on large-scale datasets, balancing effectiveness with computational efficiency.