wahnerma,
There are lots of drawbacks to laser cutting titanium, depending upon the application. Laser cutting something that thick will create a large kerf on the exit side and a large heat affected zone, as TygerDawg noted. Ti is also highly reactive with oxygen, so the alpha case produced in the surrounding area will need to be removed. Also, the machine shop will demand that any remelt slag around the cut be removed before they start machining on it, since it is hard on their cutting tools.
Personally, if I needed a rough shape from Ti plate, I would prefer water jet or wire EDM over laser. Either of those methods would allow the least amount of material waste. Especially important with the current price of aero grade Ti.
Regards,
Terry