<div id="payment_draft">
    <div class="form-group col-xl-6">
        <label for="paid_value">Valor Pago</label>
        <input type="text" class="form-control money_format" name="paid_value">
    </div>
</div>

<button class="btn_add_payment">Duplicar</button>

<script type="text/javascript">

    $('.money_format').mask('#.##0,00', {reverse: true});

    $(document).on('click', '.btn_add_payment', function(){

        var payment = $('#payment_draft');
        var container = $('.payments_container'); //adiciona em outra div

        var copy = payment.clone();

        container.append(copy)
    });

</script>

$(document).on('click', '.btn_add_payment', function(){

    var payment = $('#payment_draft');
    var container = $('.payments_container'); //adiciona em outra div

    var copy = payment.clone();
    copy.find('.money_format').mask('#.##0,00', {reverse: true});

    container.append(copy)
});

$(document).on("focus", ".money_format", function() {
   $(this).mask('#.##0,00', {reverse: true});
});