So the question: is mix/master part of the song of its own life (even if separated from artist)? Or is should be considered just a "layer" of sound will help to activate some emotions from the content of original artists? Or how would you consider it related to the concept of art/emotions?
There is no fixed answer to this question. Depends on the artist and how much the artist/band gets involved in the entire process.
Remember, there are basically three stages in the creation of a song/album:
-Preprodiction: creation of the song itself (lyrics, structure, instrumentation, etc)
-Production: the recording of the song
-Postproduction: mixing and mastering
If, let’s say you have a band of five members, and each member creates the instrumentation for their own instrument (let’s use a rock band as an example, for simplicity) and then collaborate between the five of them to finalize the song, then in theory what was created there, is the core of the song and nothing added or modified to it after that should be considered intrinsic to it.
That’s how the vast majority of people perceive the process to be. It is mostly "sold" to us to be that way. However there are three prominent figures (at least in most cases, if not more than three) that fundamentally change the final song, throughout the three stages of its creation:
-Recording engineer
-Mixing engineer
-Producer
The producer is the most essential and it actively takes transformational decisions, right from the preproduction stage. The producer can tell the bassist to completely change all the bass lines in all songs, just before going into production or even during production. For the specific subject of this thread, this is very relevant, since a decision like that can stem from issues, happenings, or a new-found sources of inspiration during recording or mixing. But more on the producer, later.
A recording engineer carries the burden of capturing the possible best performance of the musician. For example, this can be simply from just telling the guitarist that another take is needed, to tricking the guitarist by telling them to improvise/experiment while secretly recording them and aggressively presenting them the different arrangement than the originally intended, to accept the new version.
Another example would be to calm a nervous singer, by changing the atmosphere and the particular technique for recording vocals, ultimately changing the inflections, energy and overall performance of the singing in the song.
An experienced recording engineer should be able to tell the singer "go an chew 10 of these candies sold in this store and your voice will sound in X way if recorded with Y microphone", and suddenly what was intended to be a dry, single vox in the middle of the mix, is now multiple off-vocals planned to be hard-panned left and right.
A mixing engineer is fundamental as he is the one that sets what instrument is the prominent one and at what point of each song. Before the mixing stage, the placement of the instruments, the character and tonality are just mere plans. Added effects, distortion, reverberation often transform the song, all of these largely responsibility of the mixing engineer. At this stage, even the structure of the song is not fully set (verse, chorus, bridge order). The mixing engineer can add pauses, repeat segments without re-recording needed, or call for re-recording of particular parts of certain instrument, which could be simply looking for a better take, a different take with different dynamics and accent or a completely different arrangement.
The producer can of course, negate, request or encourage these changes and experimentation. Most of all the producer should be a creative ally to the musicians and very importantly, capable to keep them at bay; whether is from making the rebellious drummer to arrive on time (or deciding on using a drum machine, if he doesn’t), to deciding if certain band mates record together (for technical, creative or disciplinary reasons).
In practice, all these additions to the initial core of the song, can be implemented at many different points, by either the recording or mixing engineer or the producer. The producer can be also the mixing engineer (or the recording engineer), etc. etc.
All-in-all, this is a very long answer to say that the question itself is fundamentally a misconception. The mix is not a layer nor separate from the artist, as the three roles described above are inherent to the artistry in the song.
Two real life examples:
Marilyn Manson, for the album Mechanical Animals arrived to the production stage with a very solid foundation. While recording, the producer brought an ARP 2600 synth, and decided to use it as a distortion module, instead of traditional guitar distortion. That change alone, transformed the texture and feel of the album, influencing how the layering and extra arrangements were implemented conceptually.
(As a side note, you can see in the case above that the producer didn’t get involved until the production stage)
Second example:
A producer unhappy with the synths of a rock song.
In this case the producer felt the "size" of the synth for that part of the song was all wrong. The solution: playback the recorded synth into the recording room with the speakers blasting at very high SPL, with added reverb, and capturing that with mics, and using that as the final product.
(Notice the ~artists~ sitting there, getting schooled on how to bring character and attitude to their song. So quick question: how much of what the fans will feel during that song do you attribute to the artist and how much to the producer or mixing/recording engineer?)