This method will prevent players from seeing the affected player's chat messages. Note that its is an imperfect workaround compared to blizzard's silence punishment, It pushes the text off the screen before it can be read.
Make a new trigger, set the event to "chat message", and for the event options, leave the string field blank and set the other option to partially.
If done right the trigger editor should display 'Player Any Player types a chat message containing "", matching partially.'
Add a condition, otherwise everyone's messages will be silenced. For example, you can check if the triggering player is in a specific player group or has a specific handle. The condition you add is up to you, in this case I have it check to see if the triggering player is in a specific unit group.
Add the following action:
UI - Text message
Set the message to "<n/><n/><n/><n/><n/><n/><n/><n/><n/><n/><n/><n/><n/><n/><n/><n/><n/><n/><n/><n/>" (without the ""), the player group to "all players" and the message area to "Chat"
I'm still experimenting with this but its worked in basic tests.
This is my first tutorial so if I missed anything please let me know