Andrew
This is your lucky day as what you describe fairly very easily made (assuming the size is not too large). My 'area of expertise' is mechatronics (I bet you guessed already that it wasn't woodwork from my posts and projects) and CNC machines are good examples of mechatronic devices. I have designed and built several of these things - mostly for drilling/milling circuit boards and have supervised students that have also built similar devices.
The expensive part of the job is the precision engineering of guides etc but I guess linear bearings (circa £25 each) running on lengths of silver steel (ground straight and even) would do the job nicely. See
www.rswww.com for linear bearings and guides.
Control via stepper 3 motors (£20-40 each) would be very straightforward and if you want increased precision, then feedback could easily be derived from cheapish (£35ish each) rotary shaft encoders which would provide resolutions of 0.333 of a degree of shaft rotation.
Other very expensive item will be the actuation device to drive the cutter head - toothed belts fairly cheap and pretty good when tensioned, lead screws are pricey but accurate, ball screws are the top dog but cost £££££'s
Software is free if you can program (C or VB or pascal OK)

and costly if not
Interface boards for the motors and sensors are available commercially but they are generally very simple designs and you can probably find some on the web - or I could design them if you are willing to build 'em yourself. These would cost very little for the components.
PROBLEM - if you intend to sell these then production costs are an issue + the price the market would stand + reliability of kit and software needs considerable work + CE marking and testing. Making one for yourself is very different to making a commercial product.
If anyone wants to make one for themselves, then pm me and I will provide all the help I can with hardware/software issues especially with control of motors and reading inputs into a PC or similar.