Certain fringe elements* in Israel are known for committing crimes in reaction to Palestinian attacks. This attacks have in the past included the destruction of Palestinian-owned olive groves and mosques. Is there any halachic validity to this type of behaviour?
*Normally some fringe elements of Dati Leumi (Religious Zionist)
The underlying theoretical justification - Pikuach Nefesh, saving lives by preventing attacks - is where it would come from. Whether or not this behavior accomplishes that in this context is another matter.
The most interesting aspect of the question is if the victim of the "Price-Tag" attack is decidedly not an aggressor, just happens to be in the same community as one, or someone the aggressor would rather not see harmed. In that case, it is hardly clear-cut Pikuach Nefesh. These attacks have been widely condemned by a wide range of Rabbis as against Halacha.
Rabbi Yitzhak Shapira, wrote a book attempting to argue for a Halachic justification for such behavior.
I haven't read it, but it is widely rejected.
I would note that in general it seems like, when there is a nominally religious Jewish perpetrator of these attacks, they seem to not be too interested in the Halachic justification rather than any pretext available.
Causing damage to a non-Jew's property in a "price tag" attack would require the damager to compensate the victim for damages. This is according to a majority of Poskim as quoted in "SHU"T Chevel Nachlaso" by Rabbi Ya'akov Epstein (10, 59).
Unfortunately it is all too common that some jump to assume that "nationalistic" Jews were responsible, which is frequently untrue. It was important that you noted fringe elements, though it is very often the case that such actions are committed by others (such as Arabs) in order to slander nationalistic Jews. Such behavior is widely rejected throughout society (in the Dati Leumi community and outside it), including many prominent Dati Leumi rabbis who have denounced the actions.
From Arutz-7 - One example of many - false claims of "Price-Tagging":
http://www.israelnationalnews.com/Controls/SendFriend.ashx?print=1&type=0&item=176599
Evidence: Arabs Staging 'Price Tag' Attacks, Blaming Jews
Pictures taken by K. show Arabs chopping down their own trees. Then, they painted 'Price Tag' in Hebrew. Gil Ronen For years, Jewish residents of Judea and Samaria have been accusing Arab and leftist activists of falsely blaming them for "price tag" revenge attacks that they never carried out. Now, one determined resident of Samaria appears to have found a "smoking gun", documenting how local Arabs have been damaging olive trees and then reporting the incidents to authorities and the media as "price tag" attacks carried out by local Jews.
"Price tagging" is a phenomenon associated with fringe elements of the Israeli Right, in which assailants vandalize Arab-owned property in revenge for terrorist attacks or military demolitions of Jewish homes (which are often instigated by Arab claims). On occasion, "price taggers" have targeted army property as well, in response to demolitions and other orders carried out against Jewish communities and property by Israeli authorities.
However, on a number of occasions suspected "price tag" incidents have been proven false or staged by Arab and left-wing activists, who purposely damage Arab-owned property in an attempt to blame nearby Jewish communities.
Jewish community leaders in Judea and Samaria have regularly expressed concern that "price tag" accusations are being used by left-wing and Arab extremists as part of a campaign of anti-Jewish incitement.
Those fears appear to be well-founded. Recently, a group of Jews were kidnapped and severely beaten by Arab villagers from the village of Kusra, in Samaria. The attackers justified their actions by claiming the Jewish group had been on their way to carry out a price tag attack, and were feted by left-wing activists and media personalities; the victims, meanwhile, claimed they were in fact hiking near the village when they were ambushed.
Despite the media circus having resulted in the arrest of some of the Jewish victims of the assault, no evidence of any wrongdoing on their part has been uncovered. On the contrary, the victims were unarmed at the time, and had nothing in their possession to indicate they were involved or planning any foul play.
On occasion, Jewish residents have been able to provide photographic and videotaped proof of staged provocations by Arab and leftist extremists - but this may be the most convincing evidence to date of the truth of this claim.
The investigation was started by 27-year-old "K", after he faced accusations of carrying out price tag attacks - accusations he has strenuously denied. K is a prominent member of the ''hilltop youth", a term used to describe groups of young Israeli activists committed to building in Judea and Samaria.
K - who asked not to be named - was assisted lately in his investigation by Ari Kaniel, Director of IS, a firm that provides legal and security consulting.
Kaniel persuaded K to document the provocateurs who stage the price attacks instead of confronting them, and this is precisely what he did Tuesday, when he encountered a group of Arabs staging a "price tag" attack, not far from the Jewish town of Eli, in Samaria (Shomron).
K was shocked to see a group of Arabs chopping down dozens of olive trees. Some wore Red Crescent vests, in the hope that this would allow them to enjoy a kind of immunity.
What they were doing was clearly suspicious, Kaniel said.
"This is not pruning carried out after the harvest, in which smaller branches are cut off," he told Arutz Sheva. "They chopped down the trees at the trunk."
"We are talking about dozens of trees," he added. "K. almost cried when he told me about it."
K was arrested only two months ago on suspicion that he carried out precisely this type of attack. He has been suffering from similar complaints for 10 years.
"They take the wood for use as firewood and then run to the press and say that the settlers carried out a price tag attack,” Kaniel explained. "We were sure that they would do this, and in fact, K went back to the same spot this morning and found that they had written 'Price Tag' in yellow paint on an olive tree and on a rock."
Attorney Itamar Ben-Gvir of Honenu, an NGO that assists Jews accused of nationalist crimes, said in response: "The photographs show that the Israel Police have been persecuting K unjustifiably for a long time, while in actuality, it was the Arabs who framed him. If the photos had shown Jews, they would have been arrested for the duration of the proceedings against them."
"We demand equal justice and law enforcement, even when it turns out that the entire preconception harbored by the police was wrong," he added.
Whether they are justified, they have a biblical precedent: When David was living with the Philistines, he would go out and raid Geshurites, Girzites, and Amalekites and kill them and take their stuff.
You might be able to say that Amalek may be killed on sight anywhere and you might be able to say that one may kill any politically unsubjugated goy in the land of Israel as part of the mitzva of conquest, but the passage to continues to say that David would raid as far as Egypt.
