“overflow-x:hidden” one side only?

This is how you could do it using clip-path, which replaced the deprecated clip property:

.outer {
  background-color: rgba(0,0,255,.5);
  width: 100px;
  height: 100px;
  margin: 100px;
  clip-path: inset( -100vw -100vw -100vw 0 );
}

.inner {
  background-color: rgba(255,0,0,.5);
  width: 200px;
  height: 80px;
  position: relative;
  top: 10px;
  left: -50px;
}
<div class="outer">
  <div class="inner"></div>
</div>

Note that, as of December 2017, browser support isn’t very good.

Further reading:

  • MDN: clip-path
  • CSS-Tricks: clip-path

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