The bodies of Kevin O'Hare, 15, and Colin Polland, 39, were found at Paul's Quarry in the Glassdrumman Road area near the seaside village on Saturday evening.
Mr Polland is understood to have jumped into the water at the isolated quarry in a bid to save the teen, who had got into difficulties when swimming in the quarry, but both died.
Police and emergency services were at the scene as their bodies were recovered.
Kevin was from the Dromara area of Co Down. Mr Polland was originally from Northern Ireland but had been living in England, and it is understood he was back in the region on holiday.
A police investigation is underway to determine the circumstances surrounding the deaths.
"Post-mortem examinations will be carried out in due course," a PSNI spokesman said.
Local man Eamon Binks was out walking his dogs at around 6pm when he met a young man in a distressed state, who was running for help.
"He said that his friend was under the water and then, me and my brother came sprinting up and we were the first ones here, " Eamon explained.
Along with his brother, he ran up and down the edge of the quarry but could not locate the victims due to the wind blowing on the water's surface.
"And then all of a sudden the wind just stopped. "
Eamon said it was at that point they saw the bodies of a child and an adult in the water.
He said the scene was "absolutely tragic."
The quarry is a popular spot for young people, particularly during hot weather.
South Down MP Margaret Ritchie said she was deeply saddened at the "untimely and tragic deaths".
My thoughts and prayers and those of the wider community in this constituency are with the families at this tragic time.
Margaret Ritchie SDLP MP
"My heartfelt sympathy and that of all the people goes out to the families, friends and relatives of the two men who lost their lives in such tragic circumstances in a disused quarry at the bottom of Spence Mountain in the Mournes," the former SDLP leader said.
"The people of South Down will stand shoulder to shoulder with the families at this tragic time to provide support, assistance and solidarity."
Alliance South Down Councillor Patrick Clarke added: "I would like to commend the efforts of the PSNI divers, the Fire and Rescue Service, and the coastguard who were involved in trying to rescue both men.
"This is an awful tragedy and my heartfelt sympathies go out to the families of Kevin O'Hare and Colin Polland."
Extending his sympathy to the families, Sinn Féin MLA Chris Hazzard highlighted: "There have been similar tragedies in Derry and Strabane over the past few years and more needs to be done to improve safety at large bodies of water.
"I would urge young people not to be tempted to swim in unauthorised pools of water as there are many dangers as last night tragedy has shown."
On Saturday night, DUP South Down MLA Jim Wells described the incident as an "awful tragedy", adding the local community was "shocked to learn of the loss of life of a man and boy as a result of drowning."