What is the penalty for transporting uncut diamonds with proof of ownership but not declaring goods?

Your answer depends on which border(s) in the world you cross. Typically, when one is caught 'smuggling goods' -- i.e., carrying goods with proof of ownership and not declaring them when crossing a border -- the goods are confiscated.

When you answer the question from the border authority, "Do you have anything to declare?" or "What do you have to declare?" or "What do you plan to sell/ leave in [country name]? and you are not truthful, usually, this is a major offense in the country that you enter.

Any buyer of raw diamonds which are smuggled goods could be subject to criminal prosecution, depending on the laws of the country.