Barbing hair/Barbing shop

"to barb your hair" for "having a haircut"

Men do say that they want to 'barb' their hair. The word 'barb' does not have anything to do with cutting at all let alone human's hair. 
As a noun, it means 
1.
a point or pointed part projecting backward from a main point, as of a fishhook or arrowhead.
2.
an obviously or openly unpleasant or carping remark.
3.
Botany, Zoology . a hooked or sharp bristle.
4.
Ornithology . one of the processes attached to the rachis of a feather.
5.
one of a breed of domestic pigeons, similar to the carriers or homers, having a short, broad bill. 

When used as a verb, 'barb' is used with an object like 'furnishing something with a barb'.

"barbing your hair" as an expression is not grammatical in any way.

Say,

I want to have a haircut.
NOTE: Never say I want to cut my hair.
You go for a haircut at a BARBERSHOP not a barbing saloon.