This is going to be a bit reductionist since an adequate answer to this question would require several monographs, but yes! The Mongol expansion, while vast, was checked at multiple points across Eurasia. The Mongols were unable to expand in Japan due to the “divine wind” that crushed their fleet, they encountered difficulties with local politicians and unfamiliar environments in modern-day Hungary, and they were unable to hold land in most of southeast Asia for any extended period of time.

The encounter I know most about is that of the Mongols and Mamluks in the Levant. The Mamluks and their dynasty, which overthrew the Ayyubids, was one that utilized cavalry similar to what the Mongols had. I won’t go into the details here for the sake of brevity, but at the Battle of Ain Jalut in 1260, a Mamluk army led by Baibars defeated a joint Mongol-Cilician Armenian force. The chronicles report that Baibars made use of the terrain to his advantage, using hit-and-run tactics to whittle down the Mongols before luring them into an ambush in a forested area. The result was a decisive victory for the Mamluks and the ascent of Baibars following the assassination of Qutuz. The Mongols sought to avenge their defeat at Ain Jalut several years later but these plans were ultimately unrealized.

Whether or not you want to call these defeats the result of a specific “civilization” is up to you. Environmental historians (Jared Diamond among them) like to point out that the Mongol expansions essentially stopped wherever their military ceased to function as it did on the central Asian steppes - in the heavily wooded forests of Hungary, in the Sea of Japan, in the wet and humid climate of southeast Asia. Even though the Mamluks fought with a similar style as the Mongols, their knowledge of the geography of the Levant was clearly an advantage for them at Ain Jalut.

In terms of sources about Ain Jalut, I recommend anything written by the historian Reuven Amitai, who is based out of the Hebrew University of Jerusalem. Thomas Allsen and Peter Jackson have also written much about the Mongols.