Levy Smith admitted the charge of criminal damage and was jailed when he appeared at Maidstone Crown Court on 5 November 2020.
The 31-year-old of Newnham Lane, Eastling, also admitted common assault, dangerous driving, and breaching a restraining order.
The offences all took place in August 2020 after he contacted his victim, despite a two-year restraining order prohibiting him from doing so.
He sent the woman threatening text messages, and left alarming voice messages on her mobile phone, before slashing the tyres on her car.
On 15 August he also assaulted another woman, known to him, by punching her and causing facial injuries.
Officers on routine patrol saw Smith driving in The Meads Avenue, Sittingbourne, at around 4.25pm on 31 August.
His car had visible steering defects and police requested him to stop, however he continued driving through Knightsfield Road and Vicarage Road before he stopped the car and attempted to run away.
He was then arrested and later charged with the offences.
Investigating officer PC Zoe Hallam said: ‘Smith completely ignored the restraining order which was in place and behaved in a manner to intentionally cause fear to his victim as well as assaulting another woman.
‘His behaviour is not acceptable, and I hope this outcome acts as a deterrent to others.’