Eliphaz Dow was born around 1702 in the Province of New Hampshire, the son of Joseph and Hannah Dow. He worked as a shoemaker in Hampton Falls and was married, though there are no records indicating he had children. Described as a slightly built man, Dow was not known for physical strength or aggression. He lived a modest life in the small community of Hampton Falls, where he was acquainted with many of the local residents.

On December 12, 1754, Eliphaz Dow encountered Peter Clough, a local blacksmith, at the home of Dow's brother, Noah. The two men had a longstanding feud, and Clough had recently accused Dow of killing one of his cows. During this unexpected meeting, tensions escalated, and Clough challenged Dow to settle their dispute outside. As Clough exited the house, Dow grabbed a hoe that was leaning against the door and struck Clough on the side of the head, killing him instantly.

Dow was arrested the same day and charged with murder. He pleaded self-defense but was convicted at the February 1755 term of the Superior Court. The presiding judge was Meshech Weare, who would later become New Hampshire's first governor. Dow was sentenced to death by hanging, with the execution initially scheduled for March 20, 1755. After two reprieves, the execution was carried out on May 8, 1755, in Portsmouth.

Eliphaz Dow's execution was notable as the first recorded execution of a man in what is now the state of New Hampshire. Prior to his execution, two women, Penelope Kenny and Sarah Simpson, had been executed in 1739 for the concealment of the death of their infant children. Dow's body was buried near the site of the gallows, reportedly in a shallow grave at a crossroads, as cemeteries were considered sacred and not used for those executed for crimes.