Add following few lines into your theme functions.php file:

remove_action( 'wp_head', 'print_emoji_detection_script', 7);
remove_action( 'wp_print_styles', 'print_emoji_styles');
remove_action( 'admin_print_scripts', 'print_emoji_detection_script' );
remove_action( 'admin_print_styles', 'print_emoji_styles' );

and you are all set