What you are asking for might be possible by writing your own program (e.g. in Python) to access the Google Scholar API. In fact it would make a good assignment for a Python programming / Text processing class. But unless you are a programmer with extra time on your hands, you shouldn't attempt it.
For what it's worth, I almost never use "related articles" feature of Google Scholar. The few times I did use it, there wasn't always such a close relationship, and it certainly didn't bring up the articles that I saw as most related.
I don't think there's any substitute for reading the papers, at least the important ones, to find the most salient related papers. I do this both through direct citations and also by finding key terms that I use for new Google Scholar searches.