Alyn Flynn, of Cardross Avenue, is alleged to have made the chilling threats to the woman on August 15.
Prosecutors claim that as well as swearing, acting aggressively and making the threats to kill the woman, Flynn, 48, assaulted her by headbutting her on the nose.
The Crown’s complaint says that both charges – one of assault and one of threatening or abusive behaviour – are aggravated because they involved the alleged abuse of a partner or ex-partner.
Pleas of not guilty were entered on Flynn’s behalf during a brief hearing at Greenock Sheriff Court.
A trial date has been set for October 22, with a pre-trial procedural hearing scheduled for September 30.