Thanks! I had to look up how to add a tag to the sound. This seems like a very strange and unnecesary way for Construct 2 to handle stopping sounds, but it works.
What's especially strange is, I have stopped sounds before without a tag. The following expressions worked perfectly before. I only changed them so I could add the creation/stop of sound to the activation/deactivation of the fire all in one expression.
Obj_Fire-On Created>Play Snd_Fire at Obj_Fire
Obj_Fire-On Destroyed>Stop Snd_Fire