The pillaging and looting is described in detail by Wikipedia, followed by three days of burning. However, a few structures survived, but it is only briefly mentioned anywhere on the web (in English) that it was once again destroyed in 1900 when the Eight nation alliance occupied Beijing during the Boxer Rebellion. This is not mentioned anywhere at all in any other Wikipedia page.
The citation goes to a Chinese website, so it doesn’t seem like an official source. It makes me question whether how significant 1900 was to the destruction of the old summer palace.
Sorry for using wikipedia, I presume it’s not wholly accurate / a complete account when it comes to history.
While the Boxers are not my primary area of familiarity, nevertheless I have found no reference to a second major sacking of the Summer Palace in either Paul Cohen's History in Three Keys (1997) nor David Silbey's The Boxer Rebellion and the Great Game in China (2012), and a blog post by Dr. Silbey comparing 1860 to 1900 makes no reference to it either. The one reference I can find in a reputable English-language source is James Hevia's chapter in eds. Bickers and Tiedemann, The Boxers, China, and the World, in which it is briefly noted that the looting in 1900 was across Beijing rather than only of the Summer Palace (one reason for the Summer Palace being looted in 1860 having been that it was sufficiently distinct that looting could not spill over into Beijing and affect the local populace.) Still, little is specifically said about the relative damage to the new palace. On the whole, what damage was caused must have been, relative to 1860, quite minor.