There are many ways of disabling comments in WordPress like you can enable the option (in Settings -> Discussions page) that users must be registered and logged in to comment on your website. Another option in Settings -> Discussions page allows you to automatically close comments on articles older than ‘x’ number of days.
In this tutorial we will show you how you can easily block comments or hide existing comments in your website or on per site basis in a WordPress multisite network.
Hear No Evil is a free WordPress plugin that enables site administrator to block or unblock the ability to comment.
Simply install and activate it. After activation the plugin adds its admin page on dashboard’s settings menu. From there you can block or hide comments by ticking the checkbox.