Moore was uninjured in the incident.
Marmelo was second and A Prince of Arran two lengths behind in third.
He timed his charge to perfection, taking the lead in the final strides for a third Melbourne Cup victory, with his family set to benefit from his slice of the prize money estimated at $200,000 (£110,000).
Cliffsofmoher, an Irish-trained horse, jumped well from the gate and galloped freely before suddenly slowing just as the field passed the winning post for the first time.
The Cliffsofmoher pulled up lame about 600m into the 3200m race, dropping back in the pack and eventually coming to a stop.
The jockey of The Cliffsofmoher has been praised for his heroic efforts to save his horse from suffering a painful death.
"The horse received immediate veterinary care, however it was unable to be saved due to the nature of the injury sustained".
Oil dips on worries an economic slowdown could cut fuel demand
The secretary of state also said three ongoing non-proliferation projects in Iran are exempt from sanctions . The first round of the anti-Iran bans - which had been lifted under the accord - were re-imposed in August.
The most catastrophic year for the race was 2014, when six-year-old Japanese thoroughbred Admire Rakti collapsed straight after the Melbourne Cup and died in its stall, while Araldo broke his leg on a fence after taking fright and was euthanased.
The CliffsofMoher had won $1.7 million dollars for his owners.Today, he broke his shoulder during the 2018 #MelbourneCup & died on track behind the notorious "green screen of death".Animals & #gambling money are a TOXIC mix.Another attractive horse dead.
"This was an unfortunate incident that happens infrequently, with Victoria having one of the best safety records in world racing", Jamie Stier, Racing Victoria's manager of integrity services, said in a statement.
He said: "It was an unbelievable run - I'm completely speechless".
The Cliffsofmoher is not the first horse to be put down at the Melbourne Cup.
"RSPCA Australia has long voiced its concerns about the welfare of racehorses, including the use of inhumane devices such as whips and tongue ties, as well as the risk to injury and death during races".
The horse's trainer, Aidan O'Brien, said he was relieved jokey Moore was unharmed.
"It's very sad but it could have been worse".