Software vulnerabilities are a serious and crucial concern. Typically, in a program or function consisting of hundreds or thousands of source code statements, there are only a few statements causing the corresponding vulnerabilities. Most current approaches to vulnerability labelling are done on a function or program level by experts with the assistance of machine learning tools. Extending this approach to the code statement level is much more costly and time-consuming and remains an open problem. In this paper, we propose a novel end-to-end deep learning-based approach to identify the vulnerability-relevant code statements of a specific function. Inspired by the specific structures observed in real-world vulnerable code, we first leverage mutual information for learning a set of latent variables representing the relevance of the source code statements to the corresponding function's vulnerability. We then propose novel clustered spatial contrastive learning in order to further improve the representation learning and the robust selection process of vulnerability-relevant code statements. Experimental results on real-world datasets of 200k+ C/C++ functions show the superiority of our method over other state-of-the-art baselines. In general, our method obtains a higher performance in VCP, VCA, and Top-10 ACC measures of between 3% to 14% over the baselines when running on real-world datasets in an unsupervised setting. Our released source code samples are publicly available at \href{https://github.com/vannguyennd/livuitcl}{https://github.com/vannguyennd/livuitcl.}