I understood that Sarkel was a vast Khazar hilltop limestone-bricks fortress of the type of a fortified town, located in the present-day Rostov Oblast of Russia, on the left bank of the lower Don River.
It was built by the Khazars with Byzantine assistance and supervision of the Greek architect Petronas Kamateros around 830-840 and got its name from the white limestone-bricks used in its construction ; it was probably built to defend the northeastern border and watery trade outposts of the Khaganate.
I understood from Wikipedia that the fortress was conquered (without being destroyed) by Sviatoslav I of Kiev in 965 and was renamed Belaya Vezha ("White house" in Russian), as part of his campaign to eliminate the Khazar state as a major force in its region and which included the total destruction of its capital city Atil and the reduction of the Khaganate to a small polity in Taman region that didn't last long anyway.
It was written in Wikipedia in the article Sarkel without a source that the area later conquered from the Rus by Kipchaks (I assume the Wikipedian author of this data meant Kipchaks-Cumans).
The ruins of the site lied and were massively excavated by the Russian historian and archaeologist Mikhail Artamonov and his team in the 1930s.
The entire hill and ruins were covered with water with the completion of Tsimlyansk Reservoir in 1952 so no further excavations might be possible or beneficial.
The Alchetron free encyclopedia article about Sarkel shows beautifully detailed reconstructions of the fortified town based on multiple air photographs taken before the Tsymlyansk floating.
How was the vast Khazar fortress of Sarkel destroyed?
Maybe it was destroyed by Sviatoslav I or maybe Kipchaks-Cumans destroyed it or maybe Mongols destroyed it or maybe the destruction was temporary and natural?
I give credit to English Wikipedia for learning on the subject and using their article as base for the first two passages of this question, which I since then changed per my own wording.