The DualShock controller of the PlayStation 4 is shipped with a built-in speaker that aims to enhance gaming experience through audio cues. But if you believe that controller sounds are nothing more than a gimmick, you can mute them in the console settings.
Here's how to edit the volume settings of the DualShock 4 controller.
How To Mute Your DualShock 4 Controller
You can access the volume controls by going to Settings > Devices > Controller or by doing a long press on the PS button of the controller and selecting Adjust Devices.
Once in the Controller Settings menu, select Volume Control (Speaker for DualShock 4) option and use the left key (D-Pad) to lower the volume level until the speaker is muted:
N.B. The Volume Control (Headphones) option is only available when a compatible headphone is connected to the DUALSHOCK 4 controller.