Normally it is done automatically on Gerber generation. Check the outputs. If still present, ask the fab to remove them -- the cheaper fabs may even do this automatically without notification(!).
I don't understand the last comment; "void" what, in what way? What are "AC-coupling parts"? In any case, the idea of removing ground underneath traces or parts is generally not a good idea.
To understand, you need to think in terms of transmission lines and reference planes. A signal trace over a plane has some impedance depending on trace width and height above plane.
The plane provides shielding, reducing coupling to free fields; the loop area between trace and plane is determined by height above plane, and reducing this area reduces magnetic field exposure. Likewise reducing exposed (top visible) area, trace width, reduces electric field exposure. Both fields together (in the right place and phase) gives far-field radiation coupling.
Wrap-around plane -- coax or stripline -- is best for minimal coupling. Microstrip, with one side open to space, gives a little bit of coupling. You can make antennas this way; the coupling is generally pretty low, so that a large resonant ratio is needed. Patch antennas expose more E-field, and make practical antennas. Most microstrip applications (say LVCMOS up to 100MHz, LVDS into the Gbps), the coupling is low enough to pass commercial emissions levels without additional shielding, just bare board in plastic enclosure sort of thing.
Opening ground beneath a trace, removes that shielding. If there's still plane on the far side [of the hole], stitched with vias around the perimeter, then it acts as changing the substrate height for that section, and Zo increases. If not, Zo increases even more (geometry looks more like a trace in a slotline) and radiation is significant around the resonant frequencies of the slot (folded dipole or slot antenna geometry).
The main place you might remove ground under a net, is to reduce stray capacitance for an op-amp summing node. Higher Zo means lower C and higher L.
Everywhere else, the reduced inductance or consistent impedance is usually the higher priority, and a solid plane is desired.
Tim