"cheap and chippy chopper"
Chopper -- the instrument, rather than the person
The second definition of the word chopper in the first edition of the OED looks like this:
An instrument used for cleaving or cutting up: spec. a large-bladed short-handled axe used for cutting up meat, wood, etc., a butcher's cleaver.
In 1849 Macauley called the guillotine the French "national chopper": "the long fair hair of the handsome aristocrats who had died by the national chopper" (Barere? Misc Wks 1860 II. 160).
"cheap and chippy"
The phrase "cheap and chippy chopper" in the song "I Am So Proud," as with so many other of Gilbert's phrases, doesn't quite come together. Gilbert chose the words for their rhyme, their sound, the way they scanned -- not exactly for their sense.
Sense 3 of chippy offers "Resembling a chip; as dry as a chip" and "Vulgarly applied to the physical sensations experienced after alcohol dissipation," by which I think the editors of the OED mean "hung over."
I think what Gilbert means here is "a cheap and chipped chopper," though possibly there's colloquial language here that didn't make it into the OED.
This discussion is based on the definition of the words chippy and chopper in the first edition of the Oxford English Dictionary, which requires a little explanation.
To Act I or Act II of Gilbert and Sullivan's The Mikado.
To the homepage of this Mikado website.
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(c) Copyright 1998 Sharon Cogdill, dramaturg for this production and author of this website.
College of Fine Arts and Humanities
St. Cloud State University
This URL: http://web.stcloudstate.edu/scogdill/mikado/chopper.html.
Last update: 19 May 1998.