The DCU's creation intended to standardize the NYPD's crowd control methods, as well as providing tactical, logistical support and training to the task forces.

[9] After public backlash, Chief of Department James O'Neill stated the SRG would not be involved in handling political demonstrations.

[12] In its creation, the SRG absorbed the personnel, resources and mission of the task forces, Disorder Control Unit and the Critical Incident Response Capacity.

[2] In March 2015, the NY chapter of the National Lawyer's Guild released a statement saying "the plain intent of [SRG] is to suffocate political dissent".

[9] In September, Deputy Inspector Andrew J. Lombardo, a prominent officer involved in policing protests in NYC who had been frequently accused of targeting and interrogating protestors, was assigned to the SRG as a "supervisor".

[9][13] By the end of 2015, the SRG had been deployed to suppress multiple Black Lives Matter protests, sometimes using military grade Long-range acoustic devices (LRAD) and aggressively arresting demonstrators and members of the press.

[15] The Verge obtained NYPD documents showing police camera teams were deployed to hundreds of BLM and Occupy Wall Street protests.

[14][16][17][18][19] In December 2017, the SRG initiated a no-knock raid wherein an officer shot and killed Mario Sanabria, a 69-year-old resident, who they claimed had attacked them with a sword.

[21] In January 2018, the SRG cleared people protesting the deportation of Ravidath Ragbir by Immigrations and Customs Enforcement (ICE).

New York City Council members held an oversight hearing questioning NYPD officials about the incident.

[23] One officer was transferred out of the unit and stripped of 30 vacation days after a departmental investigation found him guilty of "using excessive force to clear a crowd of protestors".

[24][25] In October, the SRG was assigned to a protest at the Metropolitan Republican Club, which had invited Gavin McInnes - the founder of the Proud Boys - to speak.

[21] In June 2020, about 300 demonstrators protesting police violence and systemic racism in Mott Haven were kettled by the SRG.

[17] In December, the New York City Department of Investigation released a report which found the NYPD had used "excessive enforcement" against protestors, suppressed lawful First Amendment assembly, and called for reducing the role of the SRG.

[32] According to a report prepared by the City Council Finance Division in March 2021, the SRG led all units in overtime expenditures.

[36] In August, a report by the NYCLU criticized the NYPD, noting that the perpetrator of the 2022 New York City Subway attack had been blocks away from dozens of officers, including the SRG, who had been deployed sweeping a homeless encampment and destroying the belongings of unhoused New Yorkers rather than searching for the shooter.

[37] In October, elected officials, civil rights groups, and grassroots organizers staged a rally at City Hall Park calling for the abolishment of the SRG.

Members of NYC for Abortion Rights were also present, saying that the SRG provided escorts for anti-choice protests but manhandled those protecting Planned Parenthood clinics.

The city agreed to pay $4–6 million to the approximately 300 demonstrators penned by police during the Mott Haven protest.

[42] SRG documents define protestors as either "peaceful" or "violent", with examples of the latter including the "BLM movement, Occupy Wall Street, and Anti-Trump Demonstrators".