You'll either have to create a plugin or add a function to your theme functions.php file.
function remove_activity_dashboard_widget() {
remove_meta_box( 'dashboard_activity', 'dashboard', 'side' );
}
// Hook into the 'wp_dashboard_setup' action to register our function
add_action('wp_dashboard_setup', 'remove_activity_dashboard_widget' );
Here is the codex page on the subject:
http://codex.wordpress.org/Dashboard_Widgets_API#Advanced:_Removing_Dashboard_Widgets