Just like wood, ivory can be cut with the same tools. From hacksaw with rough and course teeth to delicate jewelers saw and in case you need slabs; a band saw might be the right tool. For smooth cuts, it is best to have tools with more teeth and that requires low amount of sanding.
When you cut large tusk into sections, it is important to seal the ivory pores to prevent the ivory from cracking and drying out quickly. Most of the sculptors use white glue to seal the ends while the use of varnish and hot wax is not uncommon.
While cutting tusk sections, ensure that you don’t run the saw too fast through the ivory as it makes wavy cuts. Use a light hand with steady grip and speed to cut through ivory as it is very dense. After the ivory is cut, it needs to be maintained in good condition to be crafted in different forms, including sculptures, knife handles, scrimshaws and more.
The most important aspect is to retain the humidity within the ivory and carvers use mineral oil to prevent cracks and shrinkage. But this only works on thin slabs and sheets. The slabs and thin pieces are polished with mineral oil and then wiped with soft cotton cloth and zipped in plastic bags till further use. This ensures that no moisture escapes even after the ivory piece is sanded and polished, reducing the chances of cracks and shrinking.
As the lost moisture is replaced by oil and the luster is maintained as required. The key for storing ivory is about maintaining the moisture. Traditional Russian fossil ivory hunters soak the excavated tusks in water to help maintain the moisture before it is transported to carvers. See some of the most exquisite mammoth ivory carvings at http://www.mammothivory.info/