Is it possible to pull-out a section of the pie chart intact instead of
individual slices?
Maybe Ed Ferrero can work something out. He's made bubble charts into
pictures of pies before, perhaps he can make one section into a picture
of sections.
In the meantime, you could make two pie graphs embedded in a sheet, one
copied from the other, make the sections to be "pulled out" invisible
(area=None) in one, make the area not to be pulled out invisible in the
other, make their chart areas invisible (and also the legend area
invisible!) then use Alt-drag to snap them to the same position on the
spreadsheet.
Now you can drag the whole plot area (not just a slice) of one chart
away, without pulling out the sections, and it will look like the pie
chart was pulled with several sections intact.
Because you made the chart areas invisible they are see through, and
because you made the legends invisible it doesn't matter that the legend
for one shows only some slices and the legend for the other shows only
the other slices, because the two legends will superimpose to show all
the colours.
(you actually only need the chart area and legend area of the chart on
top to be see through)
This pair of charts will also respond to updating of the numbers,
although you may want to drag the pies around from time to time to make
them look right. Just don't drag the slices, as you will break them up
if you do. Drag the square area around the circular pie.