As a native English speaker (mostly of American English but influenced by British English), my largely unschooled instinct is that "separated by" is more of an observation of fact ("As we can see in the diagram, the entries are separated by commas"), and that "separated with" is more related to an instruction ("When writing...put the entries between the square brackets, separated with commas")... I think part of the reason I feel that tug toward "with" is that I'd definitely use "with" in the imperative sentence "Separate the entries with commas."
Is there language logic to back that up? And/or is my unschooled instinct simply wrong? :-)
In this case, I'm primarily interested in informal but professional American English usage.