Joseph Willis, 49, from the city, was found guilty of attempting to murder Helen Pearson, 34, near St Bartholomew's Cemetery.
The attack followed a five-year stalking campaign of Ms Pearson.
The sentencing at Exeter Crown Court came amid accusations Devon and Cornwall Police failed to properly investigate the case.
Judge Paul Darlow directed that Willis serves at least 13 years in prison before he can be considered for parole.
The court heard Ms Pearson's flat and car were targeted and abusive messages were daubed on the streets around her house.
Threatening letters were sent to her and a dead cat was left on her doorstep.
About 125 reports of stalking were logged by Devon and Cornwall Police over the course of five years before the attempted murder.
Ms Pearson said before the sentencing: "I was terribly failed. The attacks were getting worse and worse and the police failed to realise that and act."
The Independent Police Complaints Commission (IPCC) is investigating whether police missed opportunities.
The force has confirmed it is helping the IPCC with its investigation.
The force's professional standards department is also carrying out its own review of the case.
A stalker who repeatedly stabbed a woman with scissors in Exeter has been jailed for life.