You must NOT, in any case, exceed 75 slaves asigned to the Gold Mine, Steel Mine and Mill.
Both the steel mine and the gold mine would eventually deplete. You can move slaves from one to other, but at the end of the day, the only facility that would keep running it´s the Mill, and you can not put more that 75 slaves to work in it.
About depletion, in my current run I started fully manning the Mill (it´s the easiest/cheaper investment), and latter on, buy the golden mine and transfer all the workers to it, and when the Gold mine runs out, I have conquered the steel mine and transfer, again, all the workers to it. If you don´t sell wood and stockpile it you would have enough wood to sustain your workshops all the time needed to deplete both mines without need to buy wood at all.
Depletion of the mines it´s something that runs fast. Talking from the top of my head, I buy the gold Mine roughly when I Start helping Aria´s Rebellion and both were depleted (qith 75 workers) when I finished the Aria Quest. The turnout of the Gold mine it´s brutal. You get your money back, if you man it to the top, in a couple of weeks. The turnout of the steel mine it´s a lot less, but hey, it cost you no money at all...
In the gold mine it´s mandatory to build the smelter. If you don´t buy it, you get silver ore and Gold ore, and you must manually refine it at home. And for the amounts you get, it´s something just not doable.