why does the mic sound bad? could be many reasons. poor quality dac/interface, you got a dud mic, you dont have a pop filter, emi, etc. without knowing what kind of issue its hard to say what the source is.
i dont have a mixamp myself so keep that in mind. also i believe there are various versions of mixamp so connectivity may vary.
optical from console to mixamp (for game audio)
headset and headset mic to splitter. other end of splitter to headset connection on mixamp. if you had/needed an amplifier it would go between headphones and splitter (optional 3.5mm to rca r/w cord normally also needed if amp doesnt have 3.5mm input)
i believe the mixamp should have an output for the mic. should be just a standard 3.5mm cable connection on the mixamp though since the controller is 4pole likely you might need another splitter there.
at least that is how i understand it. i would suggest looking in the manual to see their recommended setup diagrams, read them then note if there is something that confuses you.