The short answer is that there is no Jewish court authorized today to try capital cases.
In order to do so, you need two prerequisites — both of which are missing:
1. The Sanhedrin (the Supreme Court/Legislative body of Sages) must be convened in the Bais HaMikdash. Since there is no Bais HaMikdash today, no court can try capital cases.
2. You need judges who have an unbroken chain of rabbinical ordination from Moshe. That chain was broken long ago. As a result, there are no judges today qualified to try capital cases.
The Wolf