The accurate delineation of tumours in radiological images like Computed Tomography is a very specialised and time-consuming task, and currently a bottleneck preventing quantitative analyses to be performed routinely in the clinical setting. For this reason, developing methods for the automated segmentation of tumours in medical imaging is of the utmost importance and has driven significant efforts in recent years. However, challenges regarding the impracticality of 3D scans, given the large amount of voxels to be analysed, usually requires the downsampling of such images or using patches thereof when applying traditional convolutional neural networks. To overcome this problem, in this paper we propose a new methodology that uses, divided into two stages, voxel sparsification and submanifold sparse convolutional networks. This method allows segmentations to be performed with high-resolution inputs and a native 3D model architecture, obtaining state-of-the-art accuracies while significantly reducing the computational resources needed in terms of GPU memory and time. We studied the deployment of this methodology in the context of Computed Tomography images of renal cancer patients from the KiTS23 challenge, and our method achieved results competitive with the challenge winners, with Dice similarity coefficients of 95.8% for kidneys + masses, 85.7% for tumours + cysts, and 80.3% for tumours alone. Crucially, our method also offers significant computational improvements, achieving up to a 60% reduction in inference time and up to a 75\% reduction in VRAM usage compared to an equivalent dense architecture, across both CPU and various GPU cards tested.