Kevin Cutter was verbally abusive to his ex partner, who he still lived with, and pushed her while their daughter and granddaughter were in the house in Sunderland last November.
Newcastle Crown Court heard the family were so afraid of his behaviour that they "fled the building".
But the court heard the 45-year-old then picked up an axe, followed them and shouted threats in their direction.
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Prosecutor Annalise Haugstad told the court: "He grabbed an axe from the cupboard and shouted 'I will show you what I can do' and followed them.
"They were absolutely terrified. He was shouting at them and moved towards them with the axe."
Cutter, of Hylton Road, Sunderland, admitted common assault and affray in relation to the incident, which happened at the end the couple's 33-year relationship.
Mr Recorder Nathan Adams sentenced him to six months behind bars with a ten- year restraining order and told him: "You started being verbally abusive, pushed your ex partner and the matter progressed.
"So afraid of what you were going to do in the house, the rest of the family fled the building.
"You picked up an axe and pursued them outside, issuing threats in their direction.
"They must have been absolutely terrified.
"This was an extremely serious matter."
Cutter also admitted a second charge of common assault after he swiped glasses from his ex's face while she was wearing them two days earlier.
Andrew Walker, defending, said there was "no excuses" for Cutter's behaviour, which was in the aftermath of a breakdown of a long relationship.
Mr Walker said Cutter, who is "ashamed", had been drinking to excess at what was an emotional period and added: "He is not a danger"
"This was not part of a pattern of domestic violence."