Cutting off a portion of the liver reduces the total number of lobules, reducing the overall function of the liver. The liver cells can replicate to create more lobules in order to regenerate liver function. However, this is not true regeneration as the form of the regenerated liver (shape) is not the same as the original liver.
The other internal organs are not made of individual units or cannot survive being punctured. Organs like the heart are uniquely shaped and designed for its function. Removal of any part would completely ruin its function. Organs that are made of individual units like the lungs (small air sacks surrounded by vessels) or kidneys (filtering units surrounded by vessels and fluid ducts) cannot be punctured. You cannot breathe properly if there is a hole in your lung and punctures could result in fluid filling the rest of your lungs. Any removal of lung has to be completely sealed, which prevents it from regenerating. Similarly, because of the large blood flow to the kidneys, injury to the kidneys could easily be fatal. Cutting off a part of the kidney means it is not sealed from leaking.