Ron Silliman pointed to these poems by Mike Smith, Anagrams of America, some striking poems made as anagrams of existing texts, landmarks of the American canon.
Anagrammatical recycling has been done relatively rarely with musical sources, perhaps due to the close association between tonal function and form and the prevailing aesthetic which maintains this association. If I understand correctly (I know it only by reputation), Christopher Hobb's The Remorseless Lamb (1970) is a random anagram of Bach's Sheep May Safely Graze, the four voices present in any measure of Hobb's piece coming from four different places in the source. Re-combining materials from existing sources is, of course, a strategy in algorithmic composition, the projects of David Cope, for example, but I am unaware of any such example that uses the complete rearrangement of a single source. There are clearly rich possibilities to explore.