On Samsung devices with at least Android 9 (One UI) it is unfortunately not possible to directly disable the sound on screenshot, but to turn off the sound, the system sounds must be set to Silent.

Android 10 | One UI 2.0
Step 1:  Open the  Settings
Step 2:  Tap on  Sounds and vibration
Step 3:  Tap on  Volume
Step 4:  Move the  slider  to the far left
  1. Open the Settings
  2. Tap on Sounds and vibration
  3. Tap on Volume
  4. Move the slider to the far left

Samsung Instructions
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