The short answer is yes. We have one primary source that documents something like this case.

Genghis Khan was not directly responsible for destroying the damn. Jochi, Chaghatai, and Ögedei led the siege of Gurganj. The city of Gurganj was destroyed by a flood due to the destruction of a damn on the Amu Darya river.

J. J. Saunders' The History of the Mongol Conquests tells us that Genghis' three sons, Jochi, Chagatai, and Ögedei were in charge of the siege of the city. He writes:

The siege was laboriously prolonged for seven months (October 1220 - April 1221); the attackers suffered heavy losses, and soem blame for this probably attaches to a quarrel between Jochi and Chagatai which forced Chingis to intervene and place them both under the command of Ögedei. When Gurganj finally fell, the Mongols broke the dams and flooded the town, enslaved the women and children, deported the artisans to the number, it is said, of 100,000 and slew the rest......the dams were never repaired (perhaps no one could repair them), and the Oxus [Amu Darya], having been diverted from its normal course, flowed into the Caspian for 300 years.

Saunders cites the following for this passage:

On the changing course of the Oxus, consult Le Strange, 455-8, and the EI article 'Amu Darya'. Since the sixteenth century the river has emptied into the Aral Sea.

Notice that there isn't a source for the actual event of breaking the dams? Not to worry! I've found it in another book!

Leo de Hartog's Genghis Khan: Conqueror of the World states:

The town [Gurganj] fell in April 1221. The misery which had been inflicted upon Transoxania was now the lot of Gurganj. A large number of artisans were sent off to Mongolia. Children and young women were taken prisoner; the rest were massacred. The fate of the town, already ravaged by fire and plundering, as however worse than that of most other towns. Either by coincidence or by the intent of the Mongols, the dike along the Amu Darya broke. A large part of the town was flooded and many of those who had survived the massacred drowned.

De Hartog cites Vasily Barthold's work, Turkestan down to the Mongol Invasion, published in 1928. This text is available online via this link. On page 436 of the book, you'll see a reference to Ibn al-Athir. He was a chronicler who was a contemporary of the Mongols. It is likely that he wrote down this incident after hearing it from someone, though he may have actually witnessed it himself. That point is debatable. What we do know is that we have a document written in the same logical time period as the siege of Gurganj. This is the best source we have for this particular incident.