It depends on the type of thing you're trying to minimise. A low-cost lifestyle is not synonymous with a minimalist one, they are related goals but different on a practical level. Some kinds of minimalism can be very expensive.
Replacing your car with a bike and a set of walking shoes will save you a tonne of money. But it might incur more effort and planning. There'll be times when the weather is rough or the distance is too great or time is too short, when having a car would have been (more money but) much less hassle. Replacing all your books with a Kindle will probably cost you because you have to buy your books all over again (you'll probably wind up in the red even if you sell all your physical books second-hand). Does going to restaurants instead of keeping food at home count as "minimalism"?