Efficient, practical and non-destructive analysis of complex mixtures is vital in many branches of chemistry. Here we present a new type of NMR experiment that allows the study of very challenging intact mixtures, in which subspectra of individual components can be extracted when other NMR means fail, for the case of a single, intact, static (constant composition) sample. We demonstrate the new approach, SCALPEL (Spectral Component Acquisition by Localized PARAFAC Extraction of Linear components), on a natural fermented beverage, beer, and other carbohydrate mixtures, obtaining individual carbohydrate component sub-spectra. This new class of NMR experiment is based on dissecting the spectrum rather than the sample, using pulse sequences tailored to generate data suitable for powerful tensor decomposition methods to allow highly complex spectra to be analyzed stepwise, one small section at a time. It has the clear potential to attack problems beyond the reach of current methods.