In speech deepfake detection (SDD), data augmentation (DA) is commonly used to improve model generalization across varied speech conditions and spoofing attacks. However, during training, the backpropagated gradients from original and augmented inputs may misalign, which can result in conflicting parameter updates. These conflicts could hinder convergence and push the model toward suboptimal solutions, thereby reducing the benefits of DA. To investigate and address this issue, we design a dual-path data-augmented (DPDA) training framework with gradient alignment for SDD. In our framework, each training utterance is processed through two input paths: one using the original speech and the other with its augmented version. This design allows us to compare and align their backpropagated gradient directions to reduce optimization conflicts. Our analysis shows that approximately 25% of training iterations exhibit gradient conflicts between the original inputs and their augmented counterparts when using RawBoost augmentation. By resolving these conflicts with gradient alignment, our method accelerates convergence by reducing the number of training epochs and achieves up to an 18.69% relative reduction in Equal Error Rate on the In-the-Wild dataset compared to the baseline.