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an instrument with a bladed head on a handle or helve, used for hewing, cleaving, chopping, etc.
Jazz Slang. any musical instrument.
the ax, Informal.

dismissal from employment:
to get the ax.
expulsion from school.
rejection by a lover, friend, etc.:
His girlfriend gave him the ax.
any usually summary removal or curtailment.

to shape or trim with an ax.
to chop, split, destroy, break open, etc., with an ax:
The firemen had to ax the door to reach the fire.
Informal. to dismiss, restrict, or destroy brutally, as if with an ax:
The main office axed those in the field who didn’t meet their quota. Congress axed the budget.
Also, axe.
have an ax to grind, to have a personal or selfish motive:
His interest may be sincere, but I suspect he has an ax to grind.
variant of axi-, especially before a vowel.
axiom.
Contemporary Examples

Murphy, who has advised both John McCain and Mitt Romney, admittedly has an ax to grind.
President Obama’s Style Deficit Lloyd Grove September 17, 2013

Eight projects, from election assistance grants to Even Start, got the ax—but many more must be cut, writes Eve Conant.
The Government Programs Both Democrats and Republicans Hate Eve Conant March 1, 2011

Neither of the men connected with the hotel has any ax to grind with the Clintons.
Oops, Did She Do It Again? Niall Stanage October 13, 2009

The defense cuts would go through the orderly legislative process of putting together a budget, “using a scalpel and not an ax.”
Sequester Looms as Democrats and GOP Make Little Effort to Resolve Impasse Eleanor Clift February 5, 2013

In a statement, James Pollack dismissed Waldron as a “former staffer with an ax to grind.”
‘Bachmannistan’ Writer: Bachmann’s Supporters Deserved an Explanation Ben Jacobs August 27, 2013

Historical Examples

With this he raised his ax, but the woman laid her hand on his arm.
Christ Legends Selma Lagerlf

In leather loops on the door he found saw, ax, chisel, and hammer.
Blow The Man Down Holman Day

If he took down the saw and the ax from their hooks to inspect them, he put them back again where he had found them.
Look Back on Happiness Knut Hamsun

The pile was ordered to be built of rough wood, unpolished by the ax.
Museum of Antiquity L. W. Yaggy

He took his ax and cut down the stub, split it open, and found inside over two bushels of bugs.
Birds and Nature Vol. 11 No. 3 [March 1902] Various

n.

see axe (n.).

ax abbr.
axis

noun

Any musical instrument, esp the saxophone: He played his ax at the casino (1950s+ Jazz musicians)
A guitar (Rock and roll)

verb

To dismiss someone from a job, a team, a school, a relationship, etc; can, fire: who suggested to Reagan that Deaver be axed
To eliminate; cut: They axed a lot of useless stuff from the budget

[musical instrument sense fr the resemblance in shape between a saxophone and an ax, and possibly fr the rhyme with sax]
ask (shortwave transmission)
axiom
axis
In addition to the idiom beginning with ax