Minimalism is a lot easier when you stop thinking that you need features. I know that’s a bit weird to say, but most things on most websites are just extra junk. They’re extraneous. The site would be not only fine without them but most likely better off without them.

Whether you're talking UI or code structure, functional and elegant minimalism requires planning. Before you start laying down markup or css, sit down and write out what elements your site needs to be functional, where they will sit on a page and how you're going to achieve that layout in plain English. Minimalism in coding falls apart once you have to start adding a bunch of dependencies and exceptions to account for something you didn't anticipate - so make a conscious effort to anticipate!

User stories?

Model your audience. What do they want to do on your page, and why?

Help them achieve that as quickly and intuitively as possible.

I feel this approach can help decide what to include and what not, what to emphasize and what to hide.

Don't do it? Write expressive, rather than minimal, abstractions