Hyperspectral imaging (HSI) has emerged as a powerful remote sensing tool for mineral exploration, capitalizing on unique spectral signatures of minerals. However, traditional classification methods such as discriminant analysis, logistic regression, and support vector machines often struggle with environmental noise in data, sensor limitations, and the computational complexity of analyzing high-dimensional HSI data. This study presents HyDeMiC (Hyperspectral Deep Learning-based Mineral Classifier), a convolutional neural network (CNN) model designed for robust mineral classification under noisy data. To train HyDeMiC, laboratory-measured hyperspectral data for 115 minerals spanning various mineral groups were used from the United States Geological Survey (USGS) library. The training dataset was generated by convolving reference mineral spectra with an HSI sensor response function. These datasets contained three copper-bearing minerals, Cuprite, Malachite, and Chalcopyrite, used as case studies for performance demonstration. The trained CNN model was evaluated on several synthetic 2D hyperspectral datasets with noise levels of 1%, 2%, 5%, and 10%. Our noisy data analysis aims to replicate realistic field conditions. The HyDeMiC's performance was assessed using the Matthews Correlation Coefficient (MCC), providing a comprehensive measure across different noise regimes. Results demonstrate that HyDeMiC achieved near-perfect classification accuracy (MCC = 1.00) on clean and low-noise datasets and maintained strong performance under moderate noise conditions. These findings emphasize HyDeMiC's robustness in the presence of moderate noise, highlighting its potential for real-world applications in hyperspectral imaging, where noise is often a significant challenge.