Sometimes a mute is more appropriate than a ban or kick in a Discord server. This guide shows you how to go about setting up a "Muted" role for your Discord server.
Firstly, navigate to your "Server Settings" (top left):
Next, press the "Roles" button and add a new role:
After adding a new role, you can name it whatever you like, we've called our role "Muted".
You will then need to disallow the muted role from sending messages in each individual category (or channel). It isn't possible to set a server permission based global mute without changing @everyone's permissions, which is why you need to modify the permissions of each individual category or channels. To do this, right click each category or channel and click "Edit Category" (or "Edit Channel"):
After clicking edit category or channel, select the "Permissions" tab and add the muted role:
Then, after making sure you're editing the muted role's permissions, toggle off the "Send Messages" permission and save. This will make it so that role cannot send messages. See pictured:
If you chose to do this via category permissions, rather than channels, you may need to sync channel permissions. Otherwise, after making those changes for all categories (or channels), the muted role will be fully functional.
After setting this up, to mute a member of your Discord server, simply give them this role: