How complex is your scene? The work needed for a patch or surface object is more than the work needed for line graphs.
Gerd's approach has the property of not drawing portions of the graph that would extend beyond the edges. For example if you defined a plot as a straight line between two points and you want to display the middle of that line with the end-points both outside of the window, Gerd's approach would not draw the line at all.
If you have text written on the graph that would be partly inside the sub-area, do you want the fraction of the text displayed?
The easiest approach might be to copyobj() the children of the axes to the new axes, and then set the XLim and YLim properties of the new axes to show only the portion you want.
