The remote mapping of minerals and discrimination of ore and waste on surfaces are important tasks for geological applications such as those in mining. Such tasks have become possible using ground-based, close-range hyperspectral sensors which can remotely measure the reflectance properties of the environment with high spatial and spectral resolution. However, autonomous mapping of mineral spectra measured on an open-cut mine face remains a challenging problem due to the subtleness of differences in spectral absorption features between mineral and rock classes as well as variability in the illumination of the scene. An additional layer of difficulty arises when there is no annotated data available to train a supervised learning algorithm. A pipeline for unsupervised mapping of spectra on a mine face is proposed which draws from several recent advances in the hyperspectral machine learning literature. The proposed pipeline brings together unsupervised and self-supervised algorithms in a unified system to map minerals on a mine face without the need for human-annotated training data. The pipeline is evaluated with a hyperspectral image dataset of an open-cut mine face comprising mineral ore martite and non-mineralised shale. The combined system is shown to produce a superior map to its constituent algorithms, and the consistency of its mapping capability is demonstrated using data acquired at two different times of day.