jQuery Migrate is included on all pages since WordPress version 3.6. It restores APIs and features that have been deprecated and/or removed in newer versions of jQuery.
Most WordPress sites that use up-to-date themes and plugins don't require jQuery Migrate script (jquery-migrate.js or jquery-migrate.min.js) in the front end, and thus the script can be removed. By removing it, the browser will have one less JavaScript file to download and execute. As a result, your site will load faster!
To remove jQuery Migrate script from the front end of your site, you can install the Remove jQuery Migrate plugin and then simply activate it like you would any other plugin. The plugin doesn't require any configuration.
Debugging
If you're building a theme or plugin that still requires jQuery Migrate, you should consider updating your code. To check whether your theme/plugin requires jQuery Migrate in the front end, load the development version of jQuery Migrate (jquery-migrate.js) by turning on the SCRIPT_DEBUG mode in your wp-config.php file.
define( 'SCRIPT_DEBUG', true );
The development version will generate warnings on the browser console that you can use to identify and fix problems, until you no longer need jQuery Migrate and can remove it.