Vision-Language-Action (VLA) models exhibit unprecedented capabilities for embodied intelligence. However, their extensive computational and memory costs hinder their practical deployment. Existing VLA compression and acceleration approaches conduct quantization or token pruning in an ad-hoc manner but fail to enable both for a holistic efficiency improvement due to an observed incompatibility. This work introduces SQAP-VLA, the first structured, training-free VLA inference acceleration framework that simultaneously enables state-of-the-art quantization and token pruning. We overcome the incompatibility by co-designing the quantization and token pruning pipeline, where we propose new quantization-aware token pruning criteria that work on an aggressively quantized model while improving the quantizer design to enhance pruning effectiveness. When applied to standard VLA models, SQAP-VLA yields significant gains in computational efficiency and inference speed while successfully preserving core model performance, achieving a $\times$1.93 speedup and up to a 4.5\% average success rate enhancement compared to the original model.