Cheyenne, knowing Jot Singh Kalsa's work, the handle is probably stone. It looks like malachite or maybe dark jade. The damascus pattern appears to be a tight raindrop pattern. The standard damascus materials will work. I use 1084 and 15N20. Probably in a 200 to 400 layer count. The fun part would come in the patterning. You could either drill a series ( a lot) of small indentations in the billet then flatten it to bring the pattern to the surface, or use a set of dies to press the pattern in and then grind your knife blade out. Some people call this a frog skin pattern also.
Brion
Brion Tomberlin
Anvil Top Custom Knives
ABS Mastersmith
what kind of acid is the best etchant for revealing the pattern?