The guide will start from the Big Picture Mode home screen. To get there press Alt+Enter or press the Big Picture Mode icon in the upper right. This process can also be achieved another way if you want to mostly avoid Big Picture Mode, see TL;DR

1. From the home screen, make your way to settings. Which is the cog in the upper right.
2. Now, go to Controller Settings.
3. Here, we will be looking under Detected Controllers to find your controller you want to adjust.
4. Once you have selected your detected controller, you should be able to go through Preferences now.
5. Controller should be showing that the Rumble Preference is on.
6. Switch it to Off and press Submit. Now you'll be able to enjoy your game without that pesky vibration. Be sure to return later if you wish to turn it back on for some reason.

Steam Settings
Controller
General Controller Settings
Your Detected Controller
Preferences
Turn Rumble Preference to Off
Submit
Close Big Picture Mode
Play