Comment 9 for bug 172010

for now the WORKAROUND is:
1. Duplicate the object
2. Create a mask
 a rectangle or a path
3. Select the duplicated object & the mask ( {Shift} + Click )
 placing the mask over the 'piece' to be extracted
4. Object > Clip > Set
5. Finally: select and remove the nodes from the original object.

Reference: http://inkscapetutorials.wordpress.com/2011/02/22/inkscape-faq-how-do-i-crop-in-inkscape/