In Massachusetts, Andrew Oliver (a man who agreed to implement the Stamp Act in Massachusetts) saw an office of his destroyed and his house ransacked. About two weeks later the homes of other officials were damaged, and then-Lieutenant Governor Hutchinson's house was ransacked and badly damaged. In 1770 houses that broke the embargo on British goods were marked with "importer" and attacked by mobs.

In Philadelphia, Benjamin Franklin's (who wasn't always on the side of opposition to the British and their revenue efforts) house might have been destroyed in anti-Stamp Act riots if not for Governor Galloway raising a force of eight hundred men who helped protect the house (Franklin was in London at the time and this incident probably convinced him to change his politics).

So there certainly was property damage and the threat of property damage in pre-Revolution colonial America.

(source: A Leap in the Dark by Ferling)

However, how that relates to Black Lives Matter or how one views recent protests, if it does, is beyond the scope of this subreddit to discuss. AskHistorians is about the past, not about current events.

Destruction of property and violence were both significant parts of the revolutionary-era protests in British America. Let me add a few other examples to those that GrantMK2 has already mentioned.

In New York's Stamp Act protests, the crowd broke into the Lieutenant Governor Cadwallader Colden's coach house and seized Colden's carriage and two sleds. After parading these items around the city, the crowd burned them in a large bonfire along with a caricatured image (called an effigy) of the governor himself. This bonfire was in sight of the fort where Colden was stationed with his garrison, and it was clearly intended as a threat. An anonymous protestor also affixed a letter to the fort threatening to hang Governor Colden "like Porteis upon a Sign Post, as a memento to all wicked Governors." This is a reference to John Porteous, a Scottish military officer who had been lynched by an Edinburgh crowd in 1736. For Colden's letters describing these events, see Documents Relative to the Colonial History of New York, Vol. 7 (1853-87), pp. 771-775.

In fact, there was a much longer history of British American crowds using violence and destruction of property as a political tactic. In the Knowles Riot of 1747, Boston colonists protested the impressment of local sailors by kidnapping officials, destroying most of the first floor of the House of Representatives, and burning a barge. There were also riots and rampant destruction of property in response to the White Pine Laws (which granted the British navy the right to use Americans' best pines for their ship masts) and the enforcement of customs duties such as the Sugar Act. In an age without widespread popular representation or an organized police force, these riots were considered by many to be a normal--if not always legally sanctioned--way for ordinary people to express their political opinions. For the best source on this longer history of colonial riots, see Pauline Maier, From Resistance to Revolution: Colonial Radicals and the development of American opposition to Britain, 1765-1776 (1991).

Let me make one more point about violence: while Patriots during the revolutionary era rarely killed loyalists or British officials, that does not mean that their protests were nonviolent. Let's take one frequent form of protest: tarring and feathering. A lot of Americans seem to view tarring and feathering as a quaint and silly tradition intended to embarrass loyalists, but in practice, tarring and feathering was an extremely violent and painful process. The wax used was often literally boiling before being poured on the bare skin of loyalists, and it frequently left scars for life. If you're interested in the violent aspect of the revolutionary era, I would thoroughly recommend T. H. Breen's American Insurgents, American Patriots (2010). Breen's primary argument is that the American Revolution, like most revolutions, was an extremely violent event, and should be viewed as an "insurgency" against imperial authority.