For lossy audio compression algorithms like mp3 and ogg, they use psychoacustic techniques, removing information the human ear can't hear, like very high or very low frequencies (that's why they're lossy). MP3 does something like slicing the signal in small fragments, applying some mathematical functions to them, like the Modified Discrete Cosine Transform (similar to Fourier Transform or FFT), then removing some components of it.

The technique you're describing would pretty much be equivalent of using samples and sequence them, which would be akin to reinventing the .mod format (.mod, .s3m, .xm etc)

To use samples though, you need the individual samples. To identify and extract the samples from the song would be much more difficult, unless maybe each instrument was in its own track or channel.