According to Harry's linear-gradient solution (answered Oct 14 '15 at 9:55), it says that opacity background isn't possible, I tried it and yep, it isn't.
But! I found a workaround. No it's not super optimised, but it worked. So here's my solution. Since Harry doesn't use pseudo element, we can achieve this by creating one.
Set position relative to the container and create a pseudo element with the same linear-gradient properties. In other words, just clone it. Then put a transparent background for the container, and lets say a black background for the clone. Put a position absolute on it, a z-index of -1 and an opacity value (ie. 50%). It will do the job. Again it's a workaround and it's not perfect but it works just fine.
.cut-corner {_x000D_
position: relative;_x000D_
color: white;_x000D_
background-repeat: no-repeat;_x000D_
background-image: linear-gradient(white, white), linear-gradient(white, white), linear-gradient(white, white), linear-gradient(white, white), linear-gradient(to bottom left, transparent calc(50% - 1px), white calc(50% - 1px), white calc(50% + 1px), transparent calc(50% + 1px)), linear-gradient(transparent, transparent), linear-gradient(transparent, transparent);_x000D_
background-size: 2px 100%, 2px 100%, 100% 2px, 100% 2px, 25px 25px, 100% 100%, 100% 100%;_x000D_
background-position: 0% 0%, 100% 25px, -25px 0%, 0px 100%, 100% 0%, -25px 0%, 100% 25px;_x000D_
}_x000D_
.cut-corner:after {_x000D_
content: "";_x000D_
position: absolute;_x000D_
left: 0;_x000D_
bottom: 0;_x000D_
right: 0;_x000D_
top: 0;_x000D_
z-index: -1;_x000D_
opacity: 0.5;_x000D_
background-repeat: no-repeat;_x000D_
background-image: linear-gradient(white, white), linear-gradient(white, white), linear-gradient(white, white), linear-gradient(white, white), linear-gradient(to bottom left, transparent calc(50% - 1px), white calc(50% - 1px), white calc(50% + 1px), black calc(50% + 1px)), linear-gradient(black, black), linear-gradient(black, black);_x000D_
background-size: 2px 100%, 2px 100%, 100% 2px, 100% 2px, 25px 25px, 100% 100%, 100% 100%;_x000D_
background-position: 0% 0%, 100% 25px, -25px 0%, 0px 100%, 100% 0%, -25px 0%, 100% 25px;_x000D_
}_x000D_
_x000D_
/* Just for demo */_x000D_
_x000D_
div {_x000D_
padding: 10px;_x000D_
}_x000D_
body{_x000D_
background-image: radial-gradient(circle, #3F9CBA 0%, #153346 100%);_x000D_
}
_x000D_
<div class="cut-corner">_x000D_
Some content<br>_x000D_
Some content<br>_x000D_
Some content<br>_x000D_
Some content _x000D_
</div>
_x000D_