He immigrated to the United States as a child, with his parents, and was raised in the Irish slums of New York City.
It is known that during this period, he was involved in numerous fights with Indians, alongside other miners and cowboys, although details of those events are sketchy at best.
Not long after accepting the position, Duggan disarmed a drunk who was brandishing his pistol, beating the man over the head with his own gun.
The drunk man walked outside towards the street and the two faced one another about 30 feet apart, with many saloon patrons standing by to witness.
In the gunfight that followed, the two quickly went for their pistols, but Duggan managed to shoot first, firing three bullets and hitting the man in the chest, killing him.
On February 12, 1878, Horace Austin Warner Tabor, destined to later be one of America's wealthiest men, was elected mayor.
Harrison, although thought to have a fearsome reputation, was beaten and run out of town a mere two days after his appointment.
Mayor Tabor called an emergency session of the town council, and appointed Mart Duggan to replace O'Connor.
When the magistrate objected, saying the marshal had no such authority, Duggan pulled out his gun, threw it across the desk in a spinning motion and declared they are all arrested.
In late May, 1878, Duggan arrested August Rische, one of the wealthiest mine owners in Colorado at the time, for being drunk and disorderly.
Miners John Elkins (a Black man) and Charlie Hines were quarrelling over a pot at a poker game.
Duggan was dismissed from duty as Marshal after a February, 1879 drinking binge in which he threatened passersby who looked suspicious, repeatedly waving his handgun at their faces.
On March 10, 1879, Bill and Jim Bush, businessmen and also friends to Mayor Tabor, became involved in a dispute on a vacant lot with Mortimer Arbuckle, another businessman who had evidently set up his small shanty shack business on a lot belonging to the Bush brothers.
In the heat of a physical exchange, Jim Bush pulled a pistol and shot Arbuckle, killing him.
By dawn the next day, it was apparent that trouble was again brewing, so Duggan took Jim Bush, under guard, to Denver, for safe keeping until trial.
Duggan left the Marshal's position for Leadville in April, 1879, when his term expired, stating he wished to move to Flint, Michigan with his wife.
Gangs of hoodlums began taking over businesses and city property at gun point, led by Edward Frodsham, from Brigham, Utah.
On August 8, 1879, Frodsham and friend Lee Landers, the latter an escaped convict, became involved in a gunfight in Laramie, Wyoming with two men inside Susie Parker's brothel, killing a cattle dealer named Jack Taylor.
Frodsham then moved to Leadville, and the same month of his arrival, on December 29, 1879, he shot and killed Peter Thams, a Laramie resident, after the latter argued with him over the Taylor shooting.
Lake County, Colorado Deputy Sheriff Edmund H. Watson, however, stepped in and did arrest Frodsham.
Duggan returned in late December, 1879, and immediately fired all of Kelly's deputies, hiring men of his own choosing.
Duggan continued to verbally yell at Lamb, who walked as far as the front of the Purdy Brothel, where he turned and pulled his pistol.
He left the Texas House, but had walked only a few steps on Harrison Avenue before someone approached him from behind and shot him in the back of the head, then fled.
Bailey Youngston, along with his business partners Tom Dennison and Jim Harrington and employee George Evans, were arrested for his murder, tried, but acquitted due to a lack of evidence.