When is it correct to salute with your left hand?

When you have no right arm to salute with.

When you don't have a right arm or you are incapable of moving it due to injury

I have never seen that. But I will not complaint if a veteran missing his right arm salutes with his left. Of course I wouldn't be upset if he doesn't salute at all.

never

When your pissing and your right handed?

If you don't have a right arm

when your right arm or hand been amputated

No idea

I don't believe it ever is, at least in the Army. If you are unable to use your right hand for some reason, you can simply return a superior officer's greeting or come to attention for other occasions. Granted its been a LONG time since I studied the finer points of military courtesy.

The Hand salute is given by the right hand, there is no provision in the U.S. Army to salute with the left hand. Although there is a regulation for saluting, the how to's and for are covered in the Drill and Ceremonies FM, what we all need to remember it that saluting is a courtesy, usually accompanied by the greeting of the time "good morning Sir" if one is unable to salute due to injury etc. then the greeting would be appropriate, If a person that deserves a salute and does not receive one because one is unable and insists on a salute, then I would question their leadership capabilities.