You can cut what you are talking about with a router spindle, but I don't think you will be too happy with something like a handheld router motor. I think you might be more interested in a larger spindle with more tooling capacity.
The advantage to using a router spindle is the higher RPM which is essential. Router spindles are available from companies like Perske and Columbo - to name a few.
You can run these higher end spindles with a VFD - in fact, many are installed in commercial equipment through a VFD. The VFD will likely allow you to run from single phase power source.
Scott
Consistency is a good thing....unless you're consistently an idiot.