remove $_GET-parameter from WP_List_Table::tablenav

You should consider the POST request method for your action.

Otherwise you might try to hijack the set_url_scheme filter with:

add_filter( 'set_url_scheme', 'wpse_remove_arg' );

function wpse_remove_arg( $url )
{   
    return remove_query_arg( 'do_action_xyz', $url );
}

Then you could try to narrow the scope and only run this on the corresponding table page. Further you could limit it’s affect by adding it as close to the table pagination list as possible and then remove it with:

remove_filter( 'set_url_scheme', 'wpse_remove_arg' );

as soon as possible.