I would like to eliminate functions that are unused or not related to the given context. Let's say we have:
function a(){ console.log('this is an unrelated function'); }
function b(){ console.log('world'); }
function c(){ console.log('hello' + b()); }
c();
Now a() is not used at all, and I don't need it, it just makes the script bigger. And this is actually the case with jQuery too. I'm not sure if I need that much code as jQuery has. I'm using jQuery only for highcharts and to select elements from the dom by id and class, but it would be really good to get rid of the unused functions because jQuery is just simply too big! 
Are there online tools, services, functions/methods, apps that can do this minification?
Google Closure Compiler is a JavaScript optimizer. Its an useful tool that might be combined with other Google Closure Tools.
You can use the Closure Compiler as:
Dead code removal with Google Closure Compiler:
"Compilation with ADVANCED_OPTIMIZATIONS removes code that is provably unreachable. This is especially useful in combination with large libraries. If you use only a few functions from a large library file, the compiler can remove everything except those functions from its output."
The above paragraph were extracted from Closure Compiler Docs reference.