Paul Domanski made the threats at Falkirk Police Station after he was arrested on an outstanding warrant.
Prosecutor Samanatha Brown told a court that Domanski was initially calm when led into the charge bar on Wednesday.
However, the 22-year-old then began to shout aggressively and threaten the police officers.
Domanski told them: "I'll chop up your kids with a machete. I'll wipe out your families.
"When I see you in the street, you're dead. I'll chop up your daughters."
Miss Brown said: "He continued to shout and swear at the officers for several minutes and required to be restrained and removed straight to a cell."
Domanski, from Tillicoultry, Clackmannanshire, appeared from custody at Falkirk Sheriff Court and admitted threatening and abusive behaviour.
Defence agent Abigail McMurtrie said: "He has a lengthy and unenviable record of analogous previous convictions."
She said Domanski wanted to be jailed and would not co-operate with any community-based order.
An amateur bodybuilder who told police officers he would "chop up" and "wipe out" their family members has been jailed for six months.