In the field of autonomous driving, the technology of 3D object detection using LiDAR point clouds has been widely implemented. However, existing detectors are faced with challenges due to redundant overhead when processing large amounts of background points in the depth perception field, and insufficient feature mapping in the central regions of large objects. To address these issues, this paper proposes a novel 3D object detection model, SDPSNet, which combines spatial dynamic pruning and self-attention feature diffusion to reduce data redundancy and improve the representation of central features. SDPSNet introduces a spatial dynamic pruning sparse convolution strategy to optimise the inference efficiency and data redundancy of the detector. Meanwhile, the self-attention feature diffusion module is used to effectively diffuse the features of the object edges to the central region, providing a richer and more accurate representation for modelling the centre of large objects. Extensive experimental results have been conducted on the Waymo Open, nuScenes and Argoverse2 datasets. On Argoverse2, SDPSNet achieves a 2.8% increase in mAP over the previous hybrid detector, HEDNet, while being $2.4\times $ faster. It outperforms the previously popular sparse detector FSDv2 by 2.3% in mAP and is $1.5\times $ faster. It also shows a 0.2% improvement in mAP and is $1.2\times $ faster than the current best-performing sparse detector, SAFDNet.