How to disable mail sending and processing during a backup restore

Atlassian has a page of all supported environment variables:

https://confluence.atlassian.com/adminjiraserver/recognized-system-properties-for-jira-applications-938847846.html

There are environment variables that can be set to disable various mail processes:

-Datlassian.mail.senddisabled
-Datlassian.mail.fetchdisabled
-Datlassian.mail.popdisabled

Instructions on how to apply the above are on the parent page of the above

Setting properties and options on startup | Administering Jira applications Data Center 11.3 | Atlassian Documentation