Etzion was born in 1951 in kibbutz Ein Tzurim. His father, Abraham Mintz, was a member of Lehi. He was a member of Bnei Akiva, and studied at Alon Shvut. He was a founder of Gush Emunim, and helped found Ofra, where he now lives.
Following the 1979 Egypt–Israel Peace Treaty, Etzion began to lose faith in the Israeli government. Inspired by the deathbed request of his mentor Shabtai Ben-Dov, he hatched a plot to blow up the Dome of the Rock. He and co-conspirator Menachem Livni hoped that destroying the Dome of the Rock would trigger a war between Israel and her Arab neighbors, from which only Israel would emerge victorious. This would trigger the building of the third temple and a recreation of the kingdom of Israel.
Etzion founded Hai Vekayam, a group dedicated to allowing Jewish prayer on the Temple Mount against Israeli Government restrictions and majority rabbinical opinion that Jews' entry to the site is forbidden. On several occasions, the group has organized civil disobedience wherein its members, wearing Jewish prayer shawls, attempt to ascend to the mount to pray. He also organizes annual recreations of the paschal sacrifice the day before Passover in the Abu Tor neighborhood of Jerusalem.