You do know that SDL_mixer is an extension to SDL, right? So if you're project doesn't use SDL, I'm not sure whether it works as standalone.
There are also pre-built MinGW builds of SDL_mixer.
The why does the download page offer a SDL-devel-1.2.15-mingw32.tar.gz and not a SDL_mixer-devel-1.2.15-mingw32.tar.gz ?
I could only find pre-compiled runtime libraries, not non-Visual C++ buildtime. (I can't use visual studio)
I tried early versions of my code that didn't use SDL_mixer and it worked because I had the SDL and the SDLmain files ending with .a and .la, those are the Static libs for MinGW, I couldn't find a SDL_mixer.a/SDL_mixer.la for MinGW