If you need a transparent cut out edge, you can use a rotated pseudo element as a background for the div
and position it to cut out the desired corner:
body {_x000D_
background: url(http://i.imgur.com/k8BtMvj.jpg);_x000D_
background-size: cover;_x000D_
}_x000D_
div {_x000D_
position: relative;_x000D_
width: 50%;_x000D_
margin: 0 auto;_x000D_
overflow: hidden;_x000D_
padding: 20px;_x000D_
text-align: center;_x000D_
}_x000D_
div:after {_x000D_
content: '';_x000D_
position: absolute;_x000D_
width: 1100%; height: 1100%;_x000D_
top: 20px; right: -500%;_x000D_
background: rgba(255,255,255,.8);_x000D_
transform-origin: 54% 0;_x000D_
transform: rotate(45deg);_x000D_
z-index: -1;_x000D_
}
_x000D_
<div>_x000D_
... content ...<br/>... content ...<br/>... content ...<br/>... content ...<br/>... content ...<br/>... content ...<br/>... content ...<br/>... content ...<br/>... content ...<br/>... content ...<br/>_x000D_
</div>
_x000D_
Note that this solution uses transforms and you need to add the required vendor prefixes. For more info see canIuse.
To cut the bottom right edge, you can change the top, transform and transform-origin properties of the pseudo element to:
body {_x000D_
background: url(http://i.imgur.com/k8BtMvj.jpg);_x000D_
background-size: cover;_x000D_
}_x000D_
div {_x000D_
position: relative;_x000D_
width: 50%;_x000D_
margin: 0 auto;_x000D_
overflow: hidden;_x000D_
padding: 20px;_x000D_
text-align: center;_x000D_
}_x000D_
div:after {_x000D_
content: '';_x000D_
position: absolute;_x000D_
width: 1100%; height: 1100%;_x000D_
bottom: 20px; right: -500%;_x000D_
background: rgba(255,255,255,.8);_x000D_
transform-origin: 54% 100%;_x000D_
transform: rotate(-45deg);_x000D_
z-index: -1;_x000D_
}
_x000D_
<div>_x000D_
... content ...<br/>... content ...<br/>... content ...<br/>... content ...<br/>... content ...<br/>... content ...<br/>... content ...<br/>... content ...<br/>... content ...<br/>... content ...<br/>_x000D_
</div>
_x000D_