No, it means, at least for me, an axe made of gold and silver, (though I do see where you are coming from) though "a/the gold-and-silver axe" would probably be better in that sense. At best, the original version is ambiguous.
gold and silver axes = axes, some of them made of gold and some of silver/ axes made of both gold and silver, though again "gold-and-silver axes" would be better for the latter sense, I think.
If it was meant to denote more than one axe it would need to be a plural: the gold and silver axes. Then you would not know it they were all made of both metals or some made of gold and some made of silver. But as it stands you have one axe made from both metals.