Is there a specific reason you want to remove it all? You really just need to isolate the traces... Having the extra copper on board can often be of an aid in cooling.
That said, you won't be able to do what you want in one step (well, not efficiently), but you can do it in a couple steps.
First choose a large cutter (1/8") for your router (I would not try this with a Dremel, not enough HP) - I use a variable speed Bosch Colt router. RUN pcb-gcode-setup.ulp in Eagle, and under Board, Isolation, pick 0.125 for Default, 0.5 for Maximum, and .0625 for step size.
What this does is insure there is 0.125 space between traces (the size of your bit), will machine it out to 0.5" (you may be able to go larger, but there is a limit - it won't do 1"), and will step over 0.0625" from one area to the next. This should be a pretty efficient way to take out large spaces of "waste" copper. If you don't have a lot of areas with 0.125"+ open space, you can either skip this step, or use a smaller tool.
Next change to a smaller bit, say 1/16". This time choose:
0.0625 for Default (diameter of the bit)
0.125 for Maximum (2x bit diameter)
0.0313 for step size (0.5x bit diameter)
This should make a max of two passes, and should clear out some areas that the larger tool could not reach. If it leaves some "islands" you may need to increase the Maximum up to 3x bit diameter.
Finally, change to a smaller bit if you have to, depends on your trace size and spacing. I like 0.0156" snub nose end mills. Use these settings:
0.0156 for Default
0.0313 for Maximum
0.008 for step size
This should do the final sharp edge clean up and split apart tight traces - anything at least 0.016" apart. If you have traces tighter than 0.016", you will need to go to a V-bit and play with smaller Default diameters and also with the depth of cut so that you can "create" the effect of a tiny tool by going to the depth that will machine away less than 0.016".
Also, I suggest you run Opti on the code from PCBGcode, this re-sorts the GCode moving close cuts together more, so it speeds up the machining process. You can download it from PCBGCode.org, which links to here: