We propose a novel multivariate signal denoising method that performs long-range correlation analysis of multiple modes in input data by considering inherent inter-channel dependencies of the data. That is achieved through a novel and generic multivariate extension of detrended fluctuation analysis (DFA) method - another contribution of this paper. Specifically, our proposed denoising method first obtains data driven multiscale signal representation using multivariate variational mode decomposition (MVMD) method. Then, the proposed generic multivariate DFA is used to reject the predominantly noisy modes based on their randomness scores. Finally, the denoised signal is reconstructed by summing the remaining modes albeit after the removal of the noise traces using the principal component analysis (PCA).