To me, copying involves a mechanistic approach, such as constructing the copied outcome from the source's details by following a systematic process. Mimicking, however, entails a convergent approach, where the mimicked outcome emerges from the usage of a more experimental or trial-and-error method.

This is compatible with others' claim that you cannot copy somebody else's voice, you can only mimic it; that is, you try to imitate and perfect the result it until you get the desired outcome. But you can copy somebody elses's notes; that is, you get access to the source and mechanically reproduce it piece by piece.

As an aside, mimicry is the technique used by animals (or plants) to "copy" each other's appearance or behaviour.