Currently, there is no way to mute all notifications to reporter, participants, watchers on a per issue basis in JSM.
Customer notifications can be turned off at the project level or by a customer individually via their portal settings but not by an Admin on an ad-hoc basis at the issue level.

For comparison purposes, the open-source and free helpdesk management service: Spiceworks, offers this ability.
You can select a specific ticket, choose to 'mute' it, and all email communications back and forth on that ticket will stop unless it is taken off mute.

There are several critical business process related reasons for this important functionality that cannot otherwise be accomplished with current Jira Service Management features.