clean, neat
little, small
long
straight

make
give
a high-quality blade that gives a clean cut

cut in
Using sharp scissors, make a small cut in the material.

bad, deep, nasty
little, small, tiny
He has a small cut on his finger.

minor, slight, superficial
clean
fresh, new
open
paper

have
get, suffer
She got a bad cut over her right eye.

clean
Clean the cut and cover it to prevent infection.

bandage, cover, dress
heal

heal
A clean cut heals quickly.

cut on
a cut on her hand

cut to
One man was attacked and suffered cuts to his face.

cuts and bruises, cuts and scrapes

hair (usually haircut)
short
buzz (AmE), crew

have
I've made an appointment to have a haircut.

need
give sb

cut and blow-dry

big, deep, large, major, severe, sharp, significant, substantial
draconian, dramatic, drastic, huge, massive, savage (BrE)
across-the-board, swingeing (BrE)
small
federal, government
income (esp. AmE), pay, salary, wage (esp. BrE)
expenditure, financial (BrE), spending
benefit, budget, defence/defense, education, funding, job, service, staff
cost, interest-rate, price, rate (esp. AmE), tax
proposed

round
The company has announced a new round of job cuts.

impose, make
They are planning to make substantial cuts in the service.

announce, propose
proposed tax cuts

face
accept, suffer, take
The staff have all had to take a cut in salary.

oppose, support

come into effect
The cuts will come into effect next May.

cut in
cuts in public spending

choice, expensive, good, lean, prime
cheap
cold cuts (esp. AmE)

cut of
The recipe calls for a good lean cut of beef.

get, have, take
By the time the organizers have had their cut, there won't be much left.

want
If there's money to be made from selling photos of her, she wants her cut.

cut of
He takes a cut of the profits.

thick
Make sure you cut the bread nice and thick.

thinly
cleanly, neatly
Cut the stem cleanly, just beneath a leaf joint.

easily
Sandstone cuts easily.

lengthways (esp. BrE), lengthwise
Cut the carrots in half lengthwise.

away, back, down, off, out
Some trees had been cut down.

away
They cut away all the dead branches from the tree.

back
from
into
She picked up the knife and cut into the meat.
He cut the bread into thin slices.

off
out
through
I can't cut through this wood.

cut and paste (computing)
You can cut and paste between different programs.

cut sb/sth free, cut sb/sth loose
Two survivors were cut free after being trapped for twenty minutes.

cut sb's hair short
I told the stylist I wanted my hair cut short.

cut sth into pieces
Cut the cake into six pieces.

cut sth in half, cut sth in two
She cut the loaf in two and gave me one of the halves.

cut sth open
She fell and cut her head open.

freshly cut
freshly cut flowers

considerably, dramatically, drastically, sharply, significantly
short
His career was cut short by injury.

try to
manage to
We have managed to cut our costs drastically.

be forced to, have to

by
The department has to cut its spending by 30%.

from, to
The price has been cut from €250 to €175.

drastically, severely, significantly
Social work services have been cut back drastically.

be forced to, have to

on
Local authorities have been forced to cut back on expenditure.

to
We should cut back to previous levels of spending.

Cut is used with these nouns as the subject:
knife, scissors

Cut is used with these nouns as the object:
aid, allocation, barley, beard, beef, benefit, bill, branch, bread, budget, bureaucracy, cake, calorie, card, cardboard, cheese, class, cord, corn, cost, crime, deal, deficit, diamond, dividend, duty, emission, end, engine, excise, expenditure, expense, fabric, fare, fat, figure, film, finger, fingernail, flesh, flex, flow, food, fringe, funding, gash, grant, grass, groove, hair, hay, hole, import, intake, investment, job, lawn, length, link, loaf, loss, margin, meat, nail, number, opening, pack, pastry, pay, pension, pepper, per cent, pollution, premium, price, production, rate, ration, record, red tape, ribbon, risk, rope, salary, service, slice, spending, stake, stem, stone, subsidy, support, takings, tariff, tax, taxation, text, thread, throat, tie, timber, toenail, tooth, track, traffic, truancy, turf, umbilical cord, unemployment, vegetables, vein, wage, waste, way, wheat, wire, wood, workforce