On the FILE that works CORRECTLY I

selected all objects (Ctrl+A) and the Notification Display Help Message (bottom center of the inkscape window) reads:
"
16 Objects of type
Ellipse,
Path in root...."
On the FILE you are having trouble with I selected all objects (Ctrl+A) and the Notification Display reads:
"
Path (101 nodes) selected in layer
Layer 1...."
Try the Break Apart feature on this file that won't cut.. Select the Path and the use >
Path >Break
Apart (Shift+Ctrl+K). The Notification Dispay should update and read:
"
25 objects of type
Path in layer...."
Try the cutter now, Hope it works..