In OOo Draw:
 1) Insert > Picture > From File... (any image)
 2) Create an ellipse and place it over part of the image.
 3) Select both and choose Modify > Shapes > Subtract
    -- you get the image with a hole cut out of the middle. Great.
 4) Undo
 5) Repeat with Modify > Shapes > Intersect.

Did you get the result you expected?

I expected the result to show only the part of the image covered by the ellipse,
instead it shows the "wrong" part of the image.

This is because the operation does not clip the image to the shape, but instead
fills the resulting shape with the image. If the result has a different bounding
box, the image in the result appears to be shifted and scaled, in addition to
the expected clipping.

I see that this was reported some time ago as Issue 10589, and closed as
"WORKSFORME" because the feature works as designed.

Unfortunately, the design does not provide the most useful result, which would
be to clip the image to the shape. E.g. to clip a group picture to show only one
person.

Requiring the user to get and learn external image editing software for a simple
and common clipping operation seems like a significant barrier.

I see that Inkscape implements this as a separate clip (or mask) operation, and
does not allow shapes to modify images.