Numerous studies have shown that accurate analysis of neurological disorders contributes to the early diagnosis of brain disorders and provides a window to diagnose psychiatric disorders due to brain atrophy. The emergence of geometric deep learning approaches provides a new way to characterize geometric variations on brain networks. However, brain network data suffer from high heterogeneity and noise. Consequently, geometric deep learning methods struggle to identify discriminative and clinically meaningful representations from complex brain networks, resulting in poor diagnostic accuracy. Hence, the primary challenge in the diagnosis of brain diseases is to enhance the identification of discriminative features. To this end, this paper presents a dual-attention deep manifold harmonic discrimination (DA-DMHD) method for early diagnosis of neurodegenerative diseases. Here, a low-dimensional manifold projection is first learned to comprehensively exploit the geometric features of the brain network. Further, attention blocks with discrimination are proposed to learn a representation, which facilitates learning of group-dependent discriminant matrices to guide downstream analysis of group-specific references. Our proposed DA-DMHD model is evaluated on two independent datasets, ADNI and ADHD-200. Experimental results demonstrate that the model can tackle the hard-to-capture challenge of heterogeneous brain network topological differences and obtain excellent classifying performance in both accuracy and robustness compared with several existing state-of-the-art methods.