JSFiddle - React, Tailwind, and code Playground

HTML

<div class="form-group">
    <div class="col-lg-11">
        <select class="form-control" name="data[Model][0][sl_dinamica]">
            <option value="1">Valor 1</option>
            <option value="2">Valor 2</option>
            <option value="3">Valor 3</option>
        </select> <span class="btn-apagar">Apagar</span>

    </div>
    <div class="col-lg-1"> <span class="btn-adicionar">Adicionar</span>

    </div>
</div>

CSS

span {
    padding: 5px;
    background: #ccf;
    margin: 5px 10px;
    cursor: pointer;
    float: left;
    clear: both;
}

JavaScript

$('.btn-adicionar').on('click', function () {
    var select = $(this).parent().prev().find('select:first');
    var novoSelect = select.clone().attr('name', 'novo_select');
    $(select).after(novoSelect);
});