Cannot be done without help of a plugin.
For JIRA Server, you can probably have SLA functionality on a non-Service-Desk project through the use of a plugin (ie: SLAdiator, Time to SLA and Days Elapsed Plugin). Maybe ScriptRunner for JIRA enables a workaround based on the Due Date or any other Date Custom Field.
For JIRA Cloud, I don't know of any addons that might help you.
Both for JIRA Cloud & Server, you can develop your own solution, based on REST calls to the API.
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