Roger-
I think there is a bit of a misconception here in the sense that what is known as "fossil" ivory or mammoth bone, etc. is not in the technical sense anyway fossilized (at least not completely) - that's why it can still be worked with ordinary tools and not lapidary tools as would be needed if it had become completely fossilized as dinosaur bone is. This type ivory in fact is called "fossil" - in a sense a legal term - meaning it is older than the Marine Mammal Protection Act of 1972, and is therefore legal to possess. Although affected by the groundwater and minerals it has not been replaced by them and turned into "stone" as a true fossil is.
Here's a description of the various forms of fossilization which may clarify things:
"Studying the process of fossilization, or taphonomy, can involve several varying directions. After an organism has died (regardless weather it was flora, fauna or miscellaneous others), a rare event may occur leading to the possibility of fossilization. A brief discussion of the multitude of biased events which limit the possibilities of fossilization will then be followed by the basic types of fossils that may be formed. Carbonization is one form of fossilization and is typical for such organisms as plants and insects. These fossils are a coal black film formed when the volatile organic compounds disperse from the decomposing organism and end up leaving a thin residue of carbon. Permineralization is a second type of fossil formed. The soft tissue of the organism decay away and the remaining hard parts are flooded with ground water.
Dissolved with in the water is calcium carbonate (calcite) or silicate. Which ever mineral is present precipitates out and fills the pores of the long gone organism. Cementation occurs and a "rock" is left in the place of the wood or bone or what-have-you with an amazing amount of detail preserved as well. Dissolution and replacement is a third type of fossilization and can be a step
wise progression from permineralization. In some cases, when the ground water flows into the space previously occupied by the soft tissues of the organism, the original material may dissolve away, leaving a void in the surrounding sediments. This space, which is in the shape of the organism like a jell-0 mold, quickly becomes filled with minerals and an internal mold or "stone cast" is formed. Replacement can occur if it is a per mineral fossil which is
dissolved and replaced by a secondary type of mineral. Finally,
recrystallization can be the fourth type of fossil. Shells are often
recrystallized because of the relatively unstable minerals that they comprise of to begin with."