Is the violence of the Orthodox Jews in Jerusalem on the Sabbath sanctioned by the Torah?

No it is not. And those Jews who do so are a small group of radical Jews. Please do not identify other Orthodox Jews with them.

To pick up a rock on the Sabbath is a violation of the Sabbath. It is an act of carrying. To throw that rock is an act of violence, and violence is forbidden by the Torah. That’s why Israel has shown such restraint in the face of the violence dealt them by Hamas when they were shooting shells and using suicide bombers against the Israelis.

The Torah teaches us that we must restrain our anger. The first example is that of Cain who murders his brother Abel. Like any child who lashes out, he did not use his words to negotiate what he wanted or thought he needed.

This is the sin of those who throw stones at other people on the holy day. Jerusalem does not belong to them alone, and while one can sympathize with them over seeing others desecrate the Sabbath, they have no right to do it themselves and to commit acts of violence in order to make their point. If they were to kill someone in a spree of rock throwing, that would be murder.