Clip path inset circle?

You can create hole in clip-path with this approach:

let precision = 64;
let radius = 25;
let c = [...Array(precision)].map((_, i) => {
  let a = -i/(precision-1)*Math.PI*2;
  let x = Math.cos(a)*radius + 50;
  let y = Math.sin(a)*radius + 50;
  return `${x}% ${y}%`
})

document.querySelector('div').style.clipPath = 
 `polygon(100% 50%, 100% 100%, 0 100%, 0 0, 100% 0, 100% 50%, ${c.join(',')})`;
div {
  background: blue;
  width: 200px;
  height: 200px;
}
<div></div>

or symply use resulting clip string:

div {
      background: blue;
      width: 200px;
      height: 200px;
    }
<div style="clip-path: polygon(100% 50%, 100% 100%, 0px 100%, 0px 0px, 100% 0px, 100% 50%, 75% 50%, 74.8758% 47.5108%, 74.5043% 45.0463%, 73.8893% 42.6311%, 73.0369% 40.2891%, 71.9555% 38.0437%, 70.656% 35.917%, 69.1511% 33.9303%, 67.4559% 32.1033%, 65.5872% 30.4542%, 63.5637% 28.9994%, 61.4053% 27.7532%, 59.1335% 26.7282%, 56.771% 25.9344%, 54.3412% 25.3798%, 51.8683% 25.0699%, 49.3767% 25.0078%, 46.8914% 25.194%, 44.437% 25.6268%, 42.0378% 26.3018%, 39.7178% 27.2124%, 37.5% 28.3494%, 35.4064% 29.7015%, 33.4579% 31.2555%, 31.6737% 32.9957%, 30.0717% 34.9049%, 28.6677% 36.9641%, 27.4758% 39.1529%, 26.5077% 41.4495%, 25.7731% 43.8311%, 25.2792% 46.2739%, 25.0311% 48.7539%, 25.0311% 51.2461%, 25.2792% 53.7261%, 25.7731% 56.1689%, 26.5077% 58.5505%, 27.4758% 60.8471%, 28.6677% 63.0359%, 30.0717% 65.0951%, 31.6737% 67.0043%, 33.4579% 68.7445%, 35.4064% 70.2985%, 37.5% 71.6506%, 39.7178% 72.7876%, 42.0378% 73.6982%, 44.437% 74.3732%, 46.8914% 74.806%, 49.3767% 74.9922%, 51.8683% 74.9301%, 54.3412% 74.6202%, 56.771% 74.0656%, 59.1335% 73.2718%, 61.4053% 72.2468%, 63.5637% 71.0006%, 65.5872% 69.5458%, 67.4559% 67.8967%, 69.1511% 66.0697%, 70.656% 64.083%, 71.9555% 61.9563%, 73.0369% 59.7109%, 73.8893% 57.3689%, 74.5043% 54.9537%, 74.8758% 52.4892%, 75% 50%);"></div>

You could also do this with box-shadow on :after pseudo-element

div {
  position: relative;
  width: 300px;
  height: 200px;
  overflow: hidden;
  background: url('http://planetcompas.com/live/wp-content/uploads/2013/04/2015-01-Beautiful-Planet-And-Space-4-Cool-Wallpapers-HD.jpg');
  background-size: cover;
  background-position: center;
}
div:after {
  width: 50px;
  height: 50px;
  content: '';
  border-radius: 50%;
  background: transparent;
  position: absolute;
  top: 50%;
  left: 50%;
  transform: translate(-50%, -50%);
  box-shadow: 0px 0px 0px 300px lightblue;
  transition: all 0.3s linear;
}
div:hover:after {
  opacity: 0;
}
<div></div>

I don't think you can achieve this with clip-path but you can certainly cut a hole in a div using the radial-gradient background images. This has much better browser support than clip-path too.

Note: This approach (and box-shadow ) will work only when the element that is covering the content below has a colored fill. If instead of sandybrown color, there needs to be another image on top then these approaches will not work because they don't actually cut a hole, they just mimic that effect.

.div-with-hole {
  height: 100vh;
  background: radial-gradient(circle at center, transparent 25%, sandybrown 25.5%);
  background-size: 100% 100%;
  background-position: 50% 50%;
  transition: all 2s ease;
}
.div-with-hole:hover {
  background-size: 400% 400%; /* should be 100% * (100 / transparent % of radial gradient */
}
body {
  background: url(http://lorempixel.com/800/800/nature/1);
  min-height: 100vh;
  margin: 0;
  padding: 0;
}
<div class='div-with-hole'></div>

mask can do this and it will work with any kind of background:

div {
  background: linear-gradient(blue,red);
  width: 200px;
  height: 200px;
  -webkit-mask:radial-gradient(circle 50px,transparent 98%,#fff 100%);
          mask:radial-gradient(circle 50px,transparent 98%,#fff 100%);
}
<div></div>

Can also be animated:

div {
  background: linear-gradient(blue,red);
  width: 200px;
  height: 200px;
  -webkit-mask:
    radial-gradient(farthest-side,#fff 98%,transparent 100%) center/50px 50px no-repeat,
    linear-gradient(#fff,#fff);
  -webkit-mask-composite:destination-out;
   
  mask:
    radial-gradient(farthest-side,#fff 98%,transparent 100%) center/50px 50px no-repeat,
    linear-gradient(#fff,#fff);
  mask-composite:exclude;
  transition:0.5s;
}
div:hover {
  -webkit-mask-size:290px 290px,auto;
          mask-size:290px 290px,auto;
}
<div></div>

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