She learned, and ultimately became fluent in American Sign Language at 17, before she found out she had a hearing disorder.
At age 20, she was diagnosed as having Ménière's disease, a degenerative inner ear disorder whose symptoms include fluctuating hearing loss and vertigo; both her father and older sister have Ménière's disease as well.
She grew up without any knowledge of her disease, and is therefore able to use speech as any hearing person would.
She uses an accent on the show to emphasize Daphne's hearing loss. (Wikipedia)