The expression razor gang denotes a violent street gang armed with razors.

In extended use, this expression denotes a group or body responsible for making cutbacks—in particular:
1-: (British English, railway slang) a team of investigators seeking ways of improving economy and productivity;
2-: (Australian English, colloquial) a parliamentary committee charged with investigating and reducing government spending.

Among the early occurrences that I have found of razor gang in the sense of a violent street gang armed with razors are the following:

– From The Daily Standard (Brisbane, Queensland) of Tuesday 28^th April 1925:

RAZOR GANGS.
Bookmakers Terrorised.
(AUSTRALIAN CABLE SERVICE).
London, Monday.

Razor gangs are terrorising London bookmakers.
George Kent, whose arm was recency nearly severed, was again attacked to-day.
His face was slashed from the eye to the chin. His assailants escaped.

– From the account of a “case against three young men, stated to be members of the National Fascisti, who were charged with stealing a motor van and about 8,000 copies of The Daily Herald”—published in The Western Morning News and Western Daily Mercury (Plymouth, Devon, England) of Wednesday 4^th November 1925:

Wilson was next charged with carrying a pistol without a licence. In answer to the charge he said he carried it because he had been molested by a razor gang and for his protection.

In 1927, the Razor Gang became the name of a street gang in Sydney, Australia. The following is from Truth (Sydney, New South Wales) of Sunday 12^th June 1927:

THE RAZOR GANG
Terrorists of Darlinghurst Underworld
SLASHED AND DISFIGURED VICTIMS
The “L” Slice! Do you know what it is? Have you seen a man with those terrible two slashes—forming a grotesque letter “L”—scarring his face from forehead to chin?

When you see it, know it for what it is—the brand of the Razor Gang of Darlinghurst, a band of hold-up men whose weapon is the razor, and who leave their victims with faces slashed and bleeding, to seek the shelter of the nearest hospital.
The Razor Gang! It sounds like the title of an Edgar Wallace novel, but the gang exists, and its members are fully as callous and ferocious as any crooks of fiction, as the police and medical men know only too well.
Men with slashed and sliced faces, who refuse to tell how they came by their injuries, are becoming increasingly frequent visitors to Sydney General and St. Vincent’s Hospitals.
Their terrible wounds are stitched, and they go forth to face the world bearing that frightful brand forever.
The Razor Gang has terrorised the underworld of Darlinghurst, that region of bohemia, crime and mystery. The razors its members carry in their hands are feared far more than the revolver of the ordinary crook.
Men who will defy the black muzzle of the pistol quail before the bright blade held threateningly to their cheeks.
And yet the band does not kill. They slash to disfigure only.
But, strange though it may seem, their victims dare not speak. With faces slashed open, victims refuse to speak when questioned by the police.
They know too well the fate that awaits them if once the gang learns that they have allowed resentment to get the better of discretion.

1-: These are two early occurrences of razor gang used in British-English railway slang to denote a team of investigators seeking ways of improving economy and productivity:

1.1-: From a letter about a “hare-brained scheme originated by the Derby Loco L.D.C.” ¹, by a person signing themself ‘Disgusted Trade Unionist’, published in the Derby Evening Telegraph (Derby, Derbyshire, England) of Tuesday 15^th August 1950:

I was under the impression the Railway Company employed efficiency experts, called, in the workers’ vulgar parlance, “The Razor Gang,” to eliminate wasteful methods of working by engines and men.

¹ L.D.C. is the abbreviation of Local Distribution Centre.

1.2-: From Miscellany, published in the Manchester Guardian (Manchester, Lancashire, England) of Tuesday 23^rd March 1954:

Unkindest Cut
While it may or may not be true that, as Lady Tweedsmuir ² alleged in the Commons, there are cases on British Railways “of two men doing a job which can be done by one,” it should not be true for long, at least, on the London Midland Region. Immediately after the recent wage increase (writes a correspondent) an economy commission was set up by each district to tour all stations and depots, go thoroughly into the workings, and report on the possibility of cutting staff costs. Aptly christened razor gangs by the men, the commissions’ members are usually two district inspectors, a top-grade relief stationmaster—each a long-service, practical railwayman,—and the district staff clerk. To pull the wool over the eyes of these experts is not the easiest of tasks. Consequently it is not surprising that at the first big passenger station dealt with by one commission a staff reduction of 25 was recommended.
“That’s all very well,” one can almost hear the rank and file grumble, “but the higher-ups never have a commission to investigate their jobs.” In this economy drive, however, “super razor gangs” are vetting the higher-ups in district and other offices, so that the everyday “razor gangs,” so far as their everyday jobs are concerned, may have a taste of their own medicine.

² Priscilla Buchan (née Thomson – 1915-1978), Baroness Tweedsmuir of Belhelvie, was Member of Parliament for Aberdeen South from 1946 to 1966.

2-: In Australia in 1980 (possibly from the above-mentioned British-English railway slang use), the expression razor gang became the popular appellation for the Committee of Review of Commonwealth Functions, which was charged with cutting government spending. The earliest occurrence that I have found of razor gang used in this sense is from The Age (Melbourne, Victoria) of Wednesday 7^th May 1980—Malcolm Fraser (1930-2015) was then the Prime Minister of Australia, as Leader of the Liberal Party of Australia:

Budget bids take a $1000m trim
From Michelle Grattan

Canberra.—Federal Cabinet’s “razor gang” is trying to slice about $1000 million off Ministers’ bids for the August Budget.
Cabinet’s expenditure review committee, headed by the Minister for Industry and Commerce, Mr Lynch, hopes to have interviewed most Ministers about their estimates by later this week.
The committee, which has been working for some time, met all Monday and last night, and expects to see seven or eight Ministers in a full-day session today. Its recommendations will go to the Budget Cabinet meeting in July. Ministers who disagree with these recommendations can fight the matter in the full Cabinet.
The Lynch committee is expected to leave to the Budget Cabinet meeting, the main discussion on whether, and by how much, family allowances should be raised.
The Government needs to have detailed estimates of next year’s revenue before it can consider allowances. The Social Security Minister, Senator Dame Margaret Guilfoyle, is pressing hard for a rise in these allowances, which have not been changed since they were introduced in 1976.
A boost for family allowances would be a counter to the ALP’s ³ family policy—released this week—which promises a supplement for poorer families.
Members of the expenditure review committee are the Treasurer, Mr Howard, the Finance Minister, Mr Robinson, the Minister for Primary Industry, Mr Nixon, and the Minister for Employment, Mr Viner.
It is believed the bids submitted by Ministers, which cover existing and new programmes, amount to about a 5 per cent real increase in spending. The Government wants to keep the real increase in the Budget down to about 1 per cent.
Official sources say that curbing the bids is difficult because spending has been under strict control for some years. But Ministers have no doubt thrown in some marginal proposals this year, as possible pre-election ideas.

³ ALP is the abbreviation of Australian Labor Party.