不存在所谓的“负边界半径”。如果你知道你将使用什么背景，你可以用一些before/after元素来掩盖它：

body{
background: #aaa;
padding: 60px;
}
.big{
background: #fff;
padding: 100px;
border-radius: 10px;
position: relative;
}
.small{
position:absolute;
top: 0;
left: 0;
padding: 20px;
border-radius: 10px;
background: #888;
outline: 10px solid #aaa;
}
.small:before{
content: "";
position:absolute;
top: 0;
right: -20px;
width: 20px;
height: 10px;
background: radial-gradient(circle at 100% 100%, transparent 10px, #aaa 10px);
}
.small:after{
content: "";
position:absolute;
left: 0;
bottom: -20px;
width: 10px;
height: 20px;
background: radial-gradient(circle at 100% 100%, transparent 10px, #aaa 10px);
}

<div class="big">

<div class="small">Cutted out</div>
Main content with image
</div>