A clip joint is a business that cheats its customers by charging them too much. This comes from the slang verb clip.
In standard English, the main meaning of clip is "cut”. When you clip a word, you break it in parts and keep only one. Many words in standard English are clipped forms of longer words, such as bus (from omnibus), dorm (from dormitory), and flu (from influenza).
Clipping is a popular way of making slang words out of longer words, especially if the long word is formal or difficult.
Bud — from buddy (male friend)
Burbs — from suburbs
Carbs — from carbohydrates (main nutrient in foods such as bread, potatoes, rice and pasta)
‘Cause from because
Condo from condominium (an apartment owned by the people who live in it)
[b]Congrats from congratulations
Do[/b] from hairdo
Fab from fabulous
Fave from favourite
Frat from fraternity
Glam from glamorous
Grads from graduates
‘Rents from parents
Schrooms from mushrooms
Tux from tuxedo (formal suit)
Wiz from wizard
Za from pizza

IMPORTANT TO KNOW
Some clipped words are mainly used as plurals. Examples from above include burbs, carbs, and rents. Some others are meds (medications) and the names of several muscle groups, including abs (abdominals), pecs (pectorals) and lats (laterals).
Sometimes the clipped part of a word is pronounced differently from the original word:

Limo from limousine
‘stache [ǽ] from moustache

Here are some snippets of talk:

— Congrats on the new do! Totally glam!
— Thanks. My hairdresser is a wiz.

— Hey bud! Why the tux?
— ‘Cause there’s a party at the frat tonight for new grads.

— Wow! Za with shrooms! My fave!
— Not for me, I’m trying to cut down on carbs.