From the game development world, you'll find a lot of good libraries. Obviously "mixing" doesn't tell what exactly you want to do but in a lot of games we mix tracks and sound to get some kind of ambiance so I guess it can be useful for you:
UPDATE: fmod now have a free indie license.
- FMOD http://www.fmod.org/ : might be expensive even if they have a "casual" (think "indie") license. However, it's certainly the "standard" in the industry because it's uncontestably very powerful.
- Irrklang http://www.ambiera.com/irrklang/ : have been used and recommended by several indie game developers. It's cheap, even if you buy the most expensive version.
- Bass http://www.un4seen.com/ : used in several games so good quality, but more exepensive than Irrklang while cheaper than FMOD.
- Clam http://clam-project.org/ : this is more free and flexible that the previous libraries but also might be too flexible for your need.
- CAudio https://github.com/wildicv/cAudio : wrapping OpenAL with a C++ interface and adding higher lever constructs, it might not fit your need, depends, but also I'm not sure of the quality of the library; maybe worth a try as it's the most open-source of all.
If you are not pressed by time (or want to help), there is also Plaid/Audio, a promising software audio processing library which is still a work in progress but is extracted from the engine used by SourceSelf (a game which use player's sounds -like, your voice- as input).
