You seem to be saying that "se couper" is used for "get a haircut" while "couper" (without "se") is used for "cut my own hair". Doesn't it make more sense the other way around? "Se raser" means to shave oneself, not to "get a shave" and "se laver" means to wash oneself, not to "get washed". So shouldn't "se couper" refer to cutting ones own hair?
I was explaining an isolated example, but of course you can use the pronominal instead. It's more proper. Both can be used in context. For completeness,
- couper + COD = to cut + object
- se couper = to cut oneself
- se couper les cheveux = to cut my hair
- se faire + infinitif = to have something done to yourself
- se faire couper les cheveux = to get a haircut
Don't underestimate the power of "faire."