Informal:
* Self-haircutter
* Home barber
* DIY hairdresser
* Self-stylist
Humorous:
* Hair-chopper
* Barber of their own fate
* Homegrown hairstylist
Descriptive:
* Someone who cuts their own hair
* A person who practices self-haircutting
Ultimately, the best way to describe someone who cuts their own hair depends on the context and tone you want to convey.