When building Android applications, it's common to process the JVM bytecode with ProGuard before converting it to Dex bytecode. ProGuard includes a tree-shaking step. Sometimes it's necessary to tell ProGuard about specific classes or class members that it should leave alone, if they're accessed dynamically (e.g. using java.lang.reflect or Class.forName). But it's still better than nothing.
Likewise, .NET applications for the Windows Store are compiled to native code using .NET Native, and that compilation includes a tree-shaking step. This introduces some limitations on the use of reflection. I'm guessing similar limitations will apply to the native compilation option of .NET Core.
As for JavaScript, Google's Closure Compiler can do tree-shaking. But I don't know if the Closure Compiler's advanced mode works with any of the popular JavaScript libraries or frameworks, or just Google's Closure Library.
Regarding the Closure Compiler, ClojureScript touts whole program optimization as an advantage; the ClojureScript compiler just has to play by the Google Closure rules when emitting JS to take advantage. I'm sure it is harder for users of any arbitrary off-the-shelf library to gain the benefits.
There's also rollup.js (another module bundler) that supports tree-shaking: http://rollupjs.org/
Either way, it seems like the code needs to be using ES6 modules to make it all work.
https://github.com/systemjs/builder/pull/205
ES6 modules allow devs to easily specify and import only the parts of a library that are being used. The bundler takes care of pulling in the necessary parts. No magic required.