You'll need to use something like VAC or VB-Audio.
Do bear in mind though; if you don't want to hear the music, why would your viewers? A lot of casters also use music as a bit of a crutch... letting it fill the dead air, instead of actually talking/interacting/being entertaining. It's a contributing factor for a number of casts that go dead-stick; the caster sitting there silently 95%+ of the time and just playing the game.
It's one thing to use it as fill when you're fullscreen and talking with your audience, or during an AFK break. Entirely another to leave stuff going in the background to fill boring spots for you. Plus, with the diversity of tastes, it can be helpful to leave it off and just let the viewer play their own music if they want it... with no multi-channel audio option currently available, if you're playing music that they hate, they have to decide between hearing you, or muting the song. Which is a short hop from leaving for another channel, unless they're a dedicated viewer.
