Sam Jones, prosecuting, said the two met at university, becoming "really good friends" and later "romantically involved" by being "intimate on one or two occasions".
Jones went on to work at Frome College while Ms Kirk worked as a teacher at Hayesfield Girls' School in Bath.
The court heard how Jones had turned up to her workplace and would regularly message her after she ended the relationship.
The stabbing took place when the pair agreed to meet in a lane off Dransfield Way in Bath to return gifts he had bought her.
"The attack was sustained and repeated and involved him stabbing her in the neck, face and head," Mr Jones said.
"While on the ground, he stabbed her 15 times in a brutal and frenzied attack.
"Both of her lungs were punctured. She tried to fight back and suffered multiple wounds to her hands as she grabbed at the blade.
"But for the way she fought back and for the bravery of others she would have been killed.
"He stabbed her multiple times to the neck – one of the most vulnerable parts of the human body.
The jury heard how it took five members of the public, including three university students, to drag Jones from Ms Kirk and disarm him, after which he continued trying to strangle her.
