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Showing the results of subtractive manufacturing such as milling or drilling in real time, is a non-trivial task. The V-REP video you linked to was just carving the shell of the original work piece not doing a full 3D carve. You may be able to find a good open source constructive solid geometry (CSG) library that will allow you to load a mesh and then carve it with a cylinder, to simulate milling. The challenge then will be update a model in gazebo in real time, which will require a Gazebo plugin.

In short what you want to do is possible, but is a long way from an easy task. I'd start will building a model plugin that allows a loaded 3D model to dynamically change. Then when that's working look at adding a CSG library to plugin so that another link from the Gazebo world can be used as a carving tool. It's likely that such a system will run significantly slower than real time.

Hope this points you in the right direction.