Neural Radiance Field (NeRF)-based segmentation methods focus on object semantics and rely solely on RGB data, lacking intrinsic material properties. We introduce UnMix-NeRF, a framework that integrates spectral unmixing into NeRF, enabling joint hyperspectral novel view synthesis and unsupervised material segmentation. Our method models spectral reflectance via diffuse and specular components, where a learned dictionary of global endmembers represents pure material signatures, and per-point abundances capture their distribution. For material segmentation, we use spectral signature predictions along learned endmembers, allowing unsupervised material clustering. Additionally, UnMix-NeRF enables scene editing by modifying learned endmember dictionaries for flexible material-based appearance manipulation. Extensive experiments validate our approach, demonstrating superior spectral reconstruction and material segmentation to existing methods.