The first step is to identify the kind of minerals to be removed but in most cases it Is done throigh a combination of the process of coagulation ,sedimentation and filtration.Most filtration processes adopt an ion exchange /interraction techniques that form removale particles.
Ion exchange in the form of dimenralization is one process. Reverse osmosis, nano filtration, media filtration are a few more processes. Water Chemistry will always determine which process will suite the treatment scheme.
Please clarify. Without minerals in your water you become sick, your immune system can no longer fight off the simplest pathogen. If discussing EXCESSIVE minerals of one or more elements or a known mineral compound that has been processed and now has loose ions that cause it to become a toxic substance then an appropriate ion exchange system would be a first step. ( this allows you to extract the toxic portion and excessive amounts without destroying the nutritional value of the water). If cleaning and balancing is too expensive. Try adding mineral rocks after the cleaning process. You will get the very pure water like rocky mountain pure with the correct nutrients already balanced for you. Zero chance of pathogens or toxic substances. ph will also be balanced. Yes I know. 8th grade earth science. but it still works.
The Water Softeners are charged with a high capacity polystyrene bead cation exchange resin in sodium form. When hard water passes through this resin column, the hardness forming calcium and magnesium salts are replaced with sodium salts which do not posses any hardness properties. This softening process is continuous until the material is exhausted of sodium salts when it is regenerated with a solution of common salt.