I don't know how much turquoise you are inlaying. For small amounts, you can just sand with sandpaper. Stephen Hatcher is the guru of inlaying minerals and he gives you everything you need to know (
http://www.stephenhatcher.com/). You've got a challenge if you have a lot of inlay because sanding is not practical. I tried to incorporate minerals into my segmented turning in which case sanding would not work. I thought if I used softer minerals then I should be able to use carbide tools (which has a hardness of ~9 on the Mohs hardness scale) to turn. I did manage to do this in this bowl shown in the first picture with lapis lazuli (hardness 5 - 5.5, a tad softer than turquoise) but it cost me more than $100 worth of carbide cutters. In the second picture I used pony beads as Dave Mueller suggested and it cut like butter.
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I have not given up on minerals though. At the Kansas City AAW symposium this year there was a company called Blackline from S Africa selling diamond cutters. Since diamond is the hardest material known to man, I hope it can cut my embedded minerals. I will give you a followup after I get a chance to try these cutters out.