In November, Ms Gordy became the first woman with the condition to be made an MBE.
She has been hailed an "inspirational role model" for challenging attitudes towards people with learning disabilities by her performances in theatre, film and television.
Ms Gordy received a standing ovation for her speech to fellow graduates, telling them that as a child she was told her life might be limited.
"If I believed all the things that people said I couldn't do, I would not have done any [dancing, acting and campaigning]," she said. "Don't listen to doubt... believe in yourselves."
Jane Gordy, Sarah's mother, said disability had never held her daughter back. "As far as I was concerned Sarah was going to have every experience there is and if she wants to do something, just do it," she said.
The actor said ahead of the ceremony that she was "excited" about the honorary degree and that "things were changing for people with learning disabilities".
The Mencap campaigner became the charity's first official ambassador with a learning disability in 2013.
She modelled for their "Here I Am" campaign to raise awareness and improve understanding towards the 1.4m people in the UK with a learning disability.
Mencap CEO Jan Tregelles said: "Our pride in Sarah Gordy knows no bounds. What a woman."