I doubt they just dumped people off the edge. That doesn't seem like a graceful resting place for the dead - just throw them off the edge of a sky island miles in the sky to a random place on the surface. Unless they were ignorant to the existence of the surface, which this quote suggests:
Allow me tell you about the history of
Skyloft!
Skyloft is an island that has floated
here for ages... Thousands of years.
Our ancestors have always lived on this
island, as well as the surrounding
islands in the sky.
There is an impenetrable barrier of
clouds below Skyloft. Nobody who has
fallen down through the clouds has
ever been seen again.
They say there is a vast expanse of
pure nothingness beneath the clouds!
So judging by this, yeah, they are oblivious to the surface; however it does say the barrier is "impenetrable", so why would they throw the remains down there? And yet when the clouds open, we don't see a mass remains of skeletons from the hundreds of people that probably died during all those years. I mean it's possible, but it doesn't exactly seem a graceful way of dying for what's known as a noble race.
There is, however, a Graveyard, but it's far to small to house the bodies of all the people who have died. The quote above clearly says that Skyloft has existed for "thousands of years" and if you take the populace of the Island at probably an average of a around 20 at any given generation, you'd have hundreds who have died during that time period. Plus there's only a few headstones there, so yeah, that isn't the solution either.
It is a mystery. Maybe they were taken to other Islands across the Sky, maybe cremation, or maybe a magical way to dispose of the bodies aided by the power of the Goddess.
, Not to mention the Cursed Bokoblins in Ancient Cistern that place had a heaven hell type of deal going for it
