How to fix mute button (Destroy inputted player's chat) removing their ability to chat?

I have an AdminGui with a button that is supposed to get the targetted player's chat and destroys it, basically making them unable to chat or see chat until they rejoin. However I tried it on an alt and it does not work. This is a script in ServerScriptService that is fired by the admin (the client)

elseif AdminAction == "PermMute" then
    Target:WaitForChild("PlayerGui").Chat:Destroy()

Unsure why this isn't working, what's going on? The Target is the inputted playername to do an action on