When the cell repairs the gene with extra DNA, the cell doesn't recognise the cancerous cells and regrows with healthy components.
Professor Nigel McMillan compared the breakthrough to being like a spell-checker.
"This is like adding a few extra letters into a word so the spell checker doesn't recognise it anymore. The cancer must have this gene to produce, once edited, the cancer dies.
"We looked for lots of markers, inflammation and damage, but they were perfectly fine, so this is very exciting."
The study was published in Molecular Therapy.
McMillan says while there are still many steps to go through, he has applied for a grant to begin human trials within five years.
Cervical cancer is a type of cancer that occurs in the cells of the cervix — the lower part of the uterus.
You can reduce your risk of developing cervical cancer by having screening tests and receiving a vaccine that protects against HPV infection.