Firstly, your stroke isn't actually a stroke, but rather a second shape which is slightly larger - behind the path.
Clipping masks follow the path of the topmost object, and they then make that path invisible.
If you wanted an area "clipped" (cut off), you would put the object defining the clipping area - the area you want to keep on the top and then turn it into a clipping mask.
In your scenario, I would suggest that you use an actual stroke for
everything (it'll make things simpler later on) and then you can
bring the brown box to the front in order to use it as the clipping
If you really want to make this properly, I would suggest to merge the two shapes (the ear and the head) using the Shape Builder Tool (Shift+M)
This would also make it that you didn't need clipping masks.
I made my piglet by creating a few circles and polygons (for filler), made one ear and reflected it to the other side, and then merged them all together with Shape Builder: