As a PhD student in Germany, would I retain student status for tax purposes? I am currently pursuing my masters degree in computer science from TU Munich, and I would love to pursue my PhD soon after my graduation, but I am worried about the finances at the same time. 

What I gather is I should be able to make a decent enough salary but what I do not understand clearly, is whether I would retain my student status during my PhD and enjoy reduced taxation?

With reduced taxation and few other student benefits, it could possibly mean I have a more stable financial situation.
I'm not sure where you get the idea that a CS grad student in the US makes more than a CS student in Germany. If you get a full TV-L position (100%), which many CS positions are, then your net pay after deductions starts at 25,000 € per year (roughly $34,000), and goes up from there. I know of very few US graduate students whose net income is that large—most of them may get that much as a gross salary, and are then responsible for paying taxes and health insurance out of that sum.

If you aren't trying to raise a family, or have exceptional financial circumstances, the graduate salary (it's a salary, not a stipend—as it usually is in the US) is probably more than sufficient to live anywhere in Germany. (Also, you receive full social benefits, including retirement and health insurance.)

So, salary considerations shouldn't be a significant part of your decision-making process—at least not in the sense of "can I afford to be a graduate student?" You can ask if that's a lifestyle you want to be living, compared to what's possible if you go into industry.