A major challenge faced by multi-voxel Magnetic Resonance Spectroscopy (MV-MRS) imaging is partial volume effect (PVE), where signals from two or more tissue types may be mixed within a voxel. This problem arises due to the low resolution data acquisition, where the size of a voxel is kept relatively large to improve the signal to noise ratio. We propose a novel supervised Signal Mixture Model (SMM), which characterizes the MV-MRS signal into normal, low grade (infiltrative) and high grade (necrotic) brain tissue types, while accounting for in-type variation. An optimization problem is solved based on differential equations, to unmix the tissue by estimating mixture coefficients corresponding to each tissue type at each voxel. This enables visualization of probability heatmaps, useful for characterizing heterogeneous tumors. Experimental results show an overall accuracy of 91.67% and 88.89% for classifying tumors into either low or high grade against histopathology, and demonstrate the method's potential for non-invasive computer-aided diagnosis.