Andrew Halcrow, 54, from Shetland, had to be rescued when the Elsi Arrub was badly damaged west of Cape Horn on Saturday.
A previous attempt in the 32ft boat in 2006 also ended with him having to be rescued, after he became ill off Australia.
Writing on his website, Mr Halcrow said he can still hardly believe what has happened as he was sure that the mast was well rigged and would stand up to severe weather.
He wrote: "We had been hit 12 hours before, on the Friday night, by a massive wave, which threw us over. The worst one yet. It's possible the shock load from that maybe weakened the mast as well.
"It was so brutal that at first I was sure a ship had rammed into us. If you had been in a car, you would have thought a truck had slammed into you."
On Saturday morning he was sleeping or dozing in his bunk when a wave hit the yacht and threw it onto its side with a "huge crash" before it righted itself.
Hearing "horrible creaking" coming from the deck, he went to investigate and found that the boom was on the aft guardrail.
He wrote: "There was no mast, well, there was but what was left of it was lying in a mangled heap over the port bow. I could not believe it; I simply could not believe it.
"The mast was so strongly rigged I thought it would stand up to nearly anything."
Mr Halcrow spent the next few hours getting the mast clear of the hull so that it did not punch a hole in the side or pull the vessel over.
He had to loosen the rigging so that the mast would slide into the sea.
He wrote: "It was still blowing between 30 to 40 knots and the seas were still around five metres, confused and breaking, so it wasn't a very stable platform to work on.
"I suppose it was cold and wet, and I got soaked with spray, but I never felt it. Sometimes I guess you are just too focused on other things to notice."
The VHF antenna had been on the mast, so the sailor called Falmouth Coastguard on the satellite phone, who passed his details to the Chilean coastguard.
He was picked up on Sunday afternoon by a Chilean naval helicopter, which flew him to the far southern city of Punta Arenas, around 240 miles east of the yacht's position in the south Pacific, according to his website.
The sailor is now hoping to try and rescue his yacht, though he said he does not feel the same confidence as he did in 2006 as his current location is a far more dangerous coastline with powerful onshore winds.
In a "completely bizarre twist", he has been reunited with the American sailor James Brunswick, whose own mast problems led to the recovery of the Elsi Arrub in 2007, as a plane which flew to check on him spotted Mr Halcrow's boat drifting off Australia.
The pair met in Albany where Mr Halcrow had been in hospital.
Mr Brunswick, his wife and three children were also rescued at the weekend after his yacht was "dismasted" 200 nautical miles south of the Elsi Arrub on Saturday.
They were towed to Puerto Williams in Chile.
Writing yesterday, Mr Halcrow said: "The navy ship with the family on board arrived here this afternoon and I was able to speak to James as they came ashore. He couldn't believe it either."
Mr Halcrow has previously managed to successfully sail around the world on the yacht, making a successful circumnavigation in 1998 with his brother Terry.