Ok - so is mugging a robbery or not? Sure sounds like 'forcible stealing' to me. Then deadly physical force IS justified.
In NY:
A person may not use deadly physical force upon another person under circumstances specified in subdivision one unless:
...
(b) He reasonably believes that such other person is committing or attempting to commit a kidnapping, forcible rape, forcible criminal sexual act or robbery; or
...
In NY:
A person may not use deadly physical force upon another person under circumstances specified in subdivision one unless:
...
(b) He reasonably believes that such other person is committing or attempting to commit a kidnapping, forcible rape, forcible criminal sexual act or robbery; or
...