Write a module to replace jquery with another js library
Theoretically you could use hook_js_alter() to remove all traces of jQuery (and any JS files that rely on jQuery) from the page build, and drupal_add_js() to add your replacement library/code.

Bear in mind that you would have to re-implement a lot of system/contributed javascript in your library of choice to maintain the same UI experience for your admins/users.

Also remember you'll lose access to jQuery UI so none of those widgets will be available until you provide an alternative in your new library.

All in all, it would be a lot of work to do this.