I've never used this command before but I found it in the BSL bible:
Set the game's music gain
So if you have both the console and devmode turned on ingame, then hit ~ and type sound_set_music_gain 0, that should disable all music.
This is just an educated guess, I would think setting the gain to 0 would mute the music, but I am not sure.
The other alternative involves knowing the tag names of the soundtrack that is playing and issuing a sound_looping_stop or sound_impulse_stop command. That would require some research though...