It’s surprisingly difficult to disable comments globally in WordPress.
Comments can be turned off for new posts in “Settings > Discussion” screen. However, all previously published posts would still retain their comment settings and need to be disabled individually under the “Discussion” metabox on the post edit screen (which can be very time consuming).
Disable Comments with One Click
The easiest way to turn off comments globally is actually with a plugin called “Disable Comments”, which is a free download from wordpress.org.
After enabling the plugin, you can choose to disable comments everywhere or only for specific post types. If you want the changes to be permanent, choose the “persistent mode” option before saving.
If you have chosen to make the changes permanent, the plugin can be deleted after you save the settings.
If a site was abandoned for a while or suddenly got hit by a lot of comment spam, you might want to delete all the pending comments or spam comments. For both of those scenarios, you can use a plugin called Delete Comments By Status.
Delete Comments By Status also allows you to delete “trash” comments and “approved” comments in bulk.
After enabling the plugin, go to “Settings > Delete Comments”.