您可以使用获取特定类的父元素中的所有跨度。

然后，遍历结果并简单地每个元素

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document.getElementById('remover').addEventListener('click', function()
{
  const elem = document.querySelectorAll('.main-category span');
  elem.forEach(e => e.remove());
});

<div class = "main-category">
    outside of spans<br>
    <span class="first-category">foo</span>
    <span class="last-category">bar</span>
    outside of spans<br>
</div>

<div class = "main-category">
    outside of spans<br>
    <span class="first-category">hello</span>
    <span class="last-category">world</span>
    outside of spans<br>
</div>
<button type="button" id="remover">Remove elements</button>