Yes, in the top left corner of picture slots there is an option called "No Sound".  When you click on this option a check mark appears and the sound stops.

The sound currently playing will continue until Picture Slots calls another sound at which point the noise will stop.

To turn the sound back on, remove the check mark by clicking on it again.

You will also notice two other options up there, one to turn off the "Free Games" and the other to turn off "Free Games and Wild Cards".