Accurate delineation of kidney tumours in Computed Tomography (CT) is essential for downstream quantitative analysis and precision oncology, but manual segmentation is a specialised task, time-consuming and difficult to scale. Automated 3D segmentation remains challenging because CT scans are large volumetric images, making high-resolution dense convolutional networks computationally expensive and often dependent on downsampling or patch-based inference. We propose a two-stage 3D segmentation methodology based on voxel sparsification and submanifold sparse convolutional networks (SSCNs). Stage 1 uses a low-resolution sparse network to identify a region of interest (ROI); Stage 2 applies a high-resolution sparse network for refined segmentation within the cropped ROI. This enables native high-resolution 3D processing while reducing memory use and inference time. We evaluate the method on the KiTS23 renal cancer CT dataset using 5-fold cross-validation. Our method achieved Dice similarity coefficients of 95.8% for kidneys + masses, 85.7% for tumours + cysts, and 80.3% for tumours alone, competitive with top KiTS23 approaches. In direct comparisons on the same cross-validation folds, the proposed sparse method achieves tumour + cyst and tumour-only Dice scores comparable to, and slightly higher than, a patch-based nnU-Net baseline, while consistently requiring less VRAM and shorter inference time across the tested hardware. Across the tested GPUs, our sparse model is markedly faster than both nnU-Net and the zero-shot zoom-out/zoom-in foundation model SegVol, which localises kidneys well but underperforms on small heterogeneous lesions. Compared to an equivalent dense implementation of the same architecture, the proposed sparse approach achieves up to a 60% reduction in inference time and up to a 75% reduction in VRAM usage across both CPU and the GPU configurations tested.