You can do it two ways... One on the vol control on the media center... The other is on the sound mixer of Windows. You can mute the audio for the tv-tuner. Take note my setup is Vista-64 so I'm not sure if the option i have when i run ATI-650 is similar to XP environment.
I do this all the time since i play media at the same time on my setup and mute the ones that i don't want to hear. My sources are Power DVD for HD-Video, HDTV for HD TV Shows, Creative Media Source for Playing Music.