I think you are right. In fact, I would go further and say that we don't take enough minerals overall because the food we eat has been processed too much, so we are probably deficient in a lot of other minerals. I guess what I wanted to say is that you will find more people with high dangerous copper levels than low, especially among women because of the copper they add in birth control products.
Processing absolutely does remove minerals, along with vitamins and fiber, such as when you make white flour by removing the "bran and germ" of the wheat grain. Most often, one particular part of a food is extracted, potentially subjected to high heats and/or chemical processes in order to alter the taste, consistency, shelf life, or other properties of the substance, and then combined with other such substances.
For example, a cracker might consist of flour, soybean oil (i.e. fat extracted from soybeans by soaking them in chemicals called hexanes and hydrogenated), corn syrup (sugar extracted from corn), and corn starch. The human body needs dozens of micronutrients that are easily found in a bite of a naturally-occurring food but easily absent from an artificial food, especially when the necessary sugars, fats, and starches have been sourced as cheaply and conveniently as possible for manufacturing. This isn't a value judgment, and I love eating processed foods.
Its an imprecise and catchall term, but not entirely untrue. A good example of "processed food" is refined grain (non-whole-wheat bread, etc); there, various outer layers and components of each grain are milled out, leaving just the tasty starchy inner bit. Different parts of the grain will have different vitamin content, if you take only one part you may well end up with a smaller set of vitamins overall. Its not the only reason that that's bad (whole wheat is generally recommended mostly on the basis of glycemic index), but its not necessarily trivial, either.
I would say it's not necessarily the processing, but genral lack of diversity of ingredients in mainstream food outlets and home diets. The mainstream notion of "meat and three veg" as a comprehensive meal means many don't do anything but that. Three meals a day as well, is antiquated advice. I imagine most people simply don't eat enough variety of good foods.
A fast food burger is not unhealthy just because it has bad ingredients in it, but because it lacks so much else.
