Numerous neurological disorders, including prion, Parkinson's, and Alzheimer's disease (AD), are identified as being caused by alterations in protein conformation, aggregation, and metal ion dyshomeostasis. Recent years have seen a significant increase in the exploration and study of natural products (NPs) from plant and microbial sources for their therapeutic potential against several diseases, including cancer, diabetes, cardiovascular disease, and neurodegenerative diseases. In this study, we have examined the effect of two NPs, cycloastragenol (CAG) and punicalagin (PCG), on the metal-induced oligomerization and aggregation of Aβ25–35 and PrP106–126 peptides. The peptide aggregation and inhibitory properties of both NPs were examined by the thioflavin-T (ThT) assay, MALDI-TOF, circular dichroism (CD) spectroscopy, and transmission electron microscopy (TEM). Among the two NPs, PCG significantly binds to the peptides, chelates metal ions (Cu2+ and Zn2+), inhibits peptide aggregation, substantially reduces oxidative stress, and controls the production of reactive oxygen species (ROS). Both NPs exhibited low cytotoxicity and prominently mitigated peptide-mediated cell cytotoxicity in hippocampal neuronal HT-22 cells by covalent bonding and hydrophobic interactions.