Generative Adversarial Networks (GANs) achieve excellent performance in generative tasks, such as image super-resolution, but their computational requirements make difficult their deployment on resource-constrained devices. While knowledge distillation is a promising research direction for GAN compression, effectively training a smaller student generator is challenging due to the capacity mismatch between the student generator and the teacher discriminator. In this work, we propose Student Discriminator Assisted Knowledge Distillation (SDAKD), a novel GAN distillation methodology that introduces a student discriminator to mitigate this capacity mismatch. SDAKD follows a three-stage training strategy, and integrates an adapted feature map distillation approach in its last two training stages. We evaluated SDAKD on two well-performing super-resolution GANs, GCFSR and Real-ESRGAN. Our experiments demonstrate consistent improvements over the baselines and SOTA GAN knowledge distillation methods. The SDAKD source code will be made openly available upon acceptance of the paper.