If the molar is broken into two halfs can I remove the broken internal half only?

Half a tooth. You may be too optimistic... Half a tooth supporting the biting forces that a whole tooth had trouble supporting. Consider a dental implant instead.
Question is unclear. Unfortunately it's hard to picture exactly what you are describing. Please consult with a dentist to discuss all your treatment options. Your dentist can actually see what you are talking about and then discuss what can be done, what is recommended, why it is recommended and the consequences of each treatment option.
Yes u may. If u remove the internal half, wouldn't the external half be removed too? Just a thought! follow up with your dentist.