The customer was stabbed in the right side of his abdomen and lost about a litre of blood from the wound.
The woman's injuries were deemed "severe" and included a laceration to the left side of her face and a stab wound to her upper left back which, as a result, punctured her right lung causing it to collapse and blood to flow into her chest cavity.
Despite her injuries, the female victim ran out the front doors of the restaurant and across the road to the BP service station to get help.
Meanwhile, Nelson walked out of the restaurant holding a chair, and then threw it at the front windows smashing them.
One of the victims is Nelson's ex-partner.
Dixon said his client would need further psychiatric reports completed before sentencing which was set down for November 15.
Judge Keith de Ridder convicted Nelson and remanded her in further custody until that date, however, he noted that given the pressures the mental health system was under it may need to be pushed out further.