Question?
What about Ubuntu Mate flavor have a release for System Administrator?
How does it works?
It is optimized to runs on USB stick and its desktop should be a very thin. The SA Mate desktop release will have only a web browser, Take Screenshot, Pluma, Putty SSH Client, Wireshark, Sound, Caja, System Monitor, Mate terminal, Power statistics, System (hardware, network, look and feel, personal) Administrator (login windows, printers, software updater) and control center.
This sounds more like either installing the minimal version of Ubuntu-Mate and adding a few programs via a script, or installing the main version, and removing programs via a script. Not sure if it needs a whole new 'flavor' to handle...
thank you for your feedback.
as you described, we facing some particular case: when doing apt-get remove --purge mate-utils, we remove take screenshot also. if we do not do so, apt-get remove command, we still have others applications not needed like mate dictionary.
Quick aside: Putty is a Windows app, and not needed on Linux systems where a "normal" ssh client already exists.
As someone who has, as a VM-heavy user, spent years fighting with the piles of "bloat / cruft" that Linux distros seem to insist on not only installing by default, but making impossible to remove because of bogus dependencies... I've basically given up on it.
The question you need to ask, I would suggest, is not "What would the IDEAL 'usable, role-specific' be?", but rather, "What is the 'ACTIVE harm' of the bloaty parts?".
Sometimes that harm is genuine: for example, the new GTK font chooser makes having ANY "extra" fonts installed a massive PITA, because it now takes 10 or 20 times as long to actually select a font as it used to. Or the half-dozen daemons Evolution starts even if you don't use it have an impact on the footprint of a VM that you want to run on a machine that's desperately tight on resources.
But a lot of the time, there's not actual HARM other than for the OCD-ness that some of us have, and wanting the system to be "as simple as possible, but no simpler". (Bonus points if you know who said that without having to look it up. :P). A lot of the time, an extra couple of hundred MB of RAM use is, in fact, unimportant in practice, especially in a "Live" session that's going to vanish forever as soon as you reboot; and the same goes for an extra few hundred MB of disk use.
And in those scenarios especially, I'd say @MusicalCoder has it right - but that isn't even the "important" issue. As soon as you ask for a distinct "flavor" to provide this, you're putting yourself entirely at the mercy of whoever is maintaining that flavor.
My "SA MATE", for example, would absolutely need to include iotop, and as far as I'm concerned would be worthless without that. Similarly for Synaptic, and git, and so on. Meanwhile, you might think git is a waste of space, but you need 500MB of Thai fonts, and can't do anything without emacs. No maintainer is going to be able to make both of us happy.
So yeah: I'm also in the camp of "start with mate-minimal, and add the packages you want". Not only will you get a better end result from YOUR perspective - which is the only one that matters for this - but you'll even be able to have things like your aliases, panel layouts, and so on all be "right" by default every time you boot from that stick - and that's HUGELY valuable from a comfort perspective when you've probably got enough to worry about already given that you're using a USB stick in the first place!
If you do go that route, and it works well for you, a brief tutorial for others would be great if you can find the time to write one. Personally, I would LOVE for my "repair" USB to actually boot into a desktop that I don't despise and have to spend half an hour turning into something usable every time, with useful diagnostic packages available despite the machine very likely NOT being able to reach the Internet, a sensible terminal size, no stupid beeping because I OMG used the Backspace key, and so on... 
hello, good morning.
I bookmarked your post for further reply.
have a good day!
Hello arQon,
The better way to have on hands the simplest, fin and clean linux system is get by using Debian with mate desktop. With some adjustments and so on.
These words are instructive and a kind of open-mind to teach and principal, to learn with others, even if it is a “stupid” doubt or not!
and finally, as suggestion, goes some articles for you reading. these may help you try to keep your feet on the floor.
If you to know what the word suggestion means, you already turn a better person one!
Articles:
http://www.manuel-strehl.de/var/ranting_about_linux_on_desktop.en.html
http://pdf.textfiles.com/academics/ssrn-id805287.pdf
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2471292
http://www.bookmetrix.com/detail/chapter/9303f615-f792-43ea-8805-c3c042c20d93#downloads
Maybe you shouldn't post suggestions in a public forum if you're not open for debate.
If there are packages you want to add or remove, just use a post-install script.
Or you can invent and host a Ubuntu MATE variant for every single use case this distro could have.
Ubuntu MATE Greenless because you don't like green.
This one seems to be a popular one around here 
We could fork all of upstream MATE along with its libraries, and only change that one color, republish it under a different name, and people will still find a way to complain about the shade of color chosen as the default
ha, ha, ha ha ... best joke out here.
I think we need an Ubuntu Mate for Microsoft Windows "Administrators", and it should be called "Ubuntu Mate Professional" ... and it should be run on USB like Windows can do by default...
@eno2 ... based on your post, it is clear that you do not know too much about either system administrators, nor Linux, so sorry no serious answer for you... to "became" a system administrator/ to understand Linux you have to study more...