beit din court - Is one liable for murdering after being sentenced to death?

If one was sentenced to death by a Sanhedrin. After leaving the court to his death execution he kills a bystander.

Is he liable for that murder?

If yes, is he re-judged? Or it depends on what kind of death he's sentenced to - is it more severe than Hereg (for murder), like Skilah, or less, like Chenek, since we can't administer two executions?