As of the July 2011 Update (Version Silverlight Spy supports drag-and-drop operations.

Drag and drop

All nodes in the Explorer pane that support 'Save as...' or 'Save all...' can be easily be dragged from the Silverlight Spy Explorer and dropped onto any target that support file drops.

Drag and drop of folders and files in the isolated storage is not supported yet.
Drag and drop is not available in the free edition of Silverlight Spy.