Stereo mix functionality in Android? Is there any way/app for Android that mimics the functionality of stereo mix in Windows?
Android does not have such a functionality.
Audio streams/pipes are very closed source and only the system itself has access to the data  of them. There are some apps that can stream your audio output to your PC, but they require additional software.

The problem is: You can only write to the audio output (add your sound to the mix) and
only read the microphone input (listen to what comes in).

You may go the easy way and connect a male-male audio cable to your phone's audio jack and your PC's microphone jack. That way you get your audio as easy as possible to your PC (assuming you use Skype on your PC).
There are some apps that require a rooted phone to access the system audio pipes and then will stream the audio output to AirFoil Speakers or similar (requires additional software), but because of the way they do that (rerouting all audio) you won't be able to hear what is coming out of your phone.
Also they are quite delayed (up to 5 seconds even in good networks) and require you to buy the full version just a few minutes after using them.
My suggestion:
If your device is not rooted: Try the audio cable method.
If you have a rooted device: You can try finding an app that allows you to stream the audio output to your PC.
The problem is: Audio streams are deeply embedded into the system. Normal apps can't read the audio stream of the system, except for their own data before it is played.
Worth noting: some headphones with TRRS jacks result in stereo mix recording if playing music through the headphones and recording. Even if the extra wire is not for a mic but a switch.