In the ServiceDesk Application Property settings, there is a flag called AllowAutoEscalation. You can set this to false to automatically turn off the "timeout date" for all Tickets that are created in ServiceDesk. This means that "even if SLA warn date arrives, this task will not auto escalate."
NOTE: To edit this setting, in the Process Manager portal, go to Admin -> Data -> Application Properties -> then click on the appropriate Application Properties Profile.