I've come across a problem. A few of my characters are miners, and I have almost *no idea* what miners actually do. To my knowledge, they find veins of rock where the ore they want (In this case, silver,) is prevalent. Then they hit the veins with picks or hammers or something to break chunks of ore-rich rocks out, haul those chunks out on a minecart, and smelt them. (The technology available is approximately similar to late 19th century, if that matters.) So... Am I close? What else do I need to know?
The late 19th century would have had more technological mining. Steam engines had long since been invented and did most of the moving for people. Explosives also did the early removal of layers before the manual labor actually started as well as to blast through harder rocks. Of course, there were different kinds of mines, the kind I'm describing is more like coal, which was in super high demand and in great quantity, so the infrastructure was build around it was state-of-the-art for the time. The miners migrating west in search of gold did basically what you described, manual mining had not changed must since the days of the early Roman Empire.
You need to move the ore into a foundry, pretty sure they had those. Once there, they would melt the ore and separate the silver from the impurities. From there you can have them pour the silver into ingot molds, and do what ever they wish with the final product. So I think you have it on the nose by the looks of it. Might want to use the correct terminology in your WIP, but other than that you are looking spot on.
First you you write a command script and then install it into a non-human automated device. Kidding, that only works for videogames and science fiction. In the beginning of the ninteenth century, bell pits and drift mining where mainly used to extract coal ore. Small scale shaft mining was as well. If you're doing something similar to LitRPG or fantasy, I don't see it being a huge issue to involve so much detail over the technique of extraction. I would suggest resourcing WikiPedia if you're interested in learning all of the techniques. The basics of mining is that a miner locates a vein of ore. Then using various means they extract the ore/mineral from the earth. It could be underground or located on the surface. Transportation, equipment, weight capacity, storage capacity, and various other nuisances are important factors.