How to Round Out Corners When Using CSS Clip-Path

How to keep border-radius when using clip-path?

Use mask not clip-path:

body{
background-color: black;
}

.card-oval-gradient {
position: relative;
width: 10rem;
height: 6rem;
background-color: blue;
border-radius: 0.5rem;
-webkit-mask: linear-gradient(#fff 0 0);
mask: linear-gradient(#fff 0 0);
}

.card-oval-gradient > * {
position: relative;
z-index: 2;
}

.card-oval-gradient:hover::before {
content: '';

position: absolute;
left: -7rem;
top: -10rem;
width: 18rem;
height: 28rem;
-moz-border-radius: 15rem / 20rem;
-webkit-border-radius: 15rem / 20rem;
border-radius: 15rem / 20rem;
opacity: 0.6;
transform: scaleX(-1) rotate(61deg);
background-image: linear-gradient(
138deg,
#4d3d8f 0%,
#df67ed 23%,
#e24c26 65%,
#f18823 84%,
#3aa6c2 100%
);

filter: blur(50px);
}
<div class="card-oval-gradient">
</div>

clip-path polygon rounded edge

I hope this helps you.
It was solved with the before pseudo-class and tranform skewy.

SCSS:

.test {
position: relative;
width: 75%;
height: 600px;
margin: 0 auto;

.bg {
width: 100%;
height: 483px;
position: relative;
overflow:hidden;
z-index: 0;
}

.bg:before {
content: "";
position: absolute;
background: orange;
z-index: -1;
top:0;
left:0;
bottom:0;
right:0;
border-bottom-right-radius: 120px;
transform: skewy(-4deg);
transform-origin: left bottom;
}

}

.test {  position: relative;  width: 75%;  height: 600px;  margin: 0 auto; }  .test .bg {    width: 100%;    height: 483px;    position: relative;    overflow: hidden;    z-index: 0; }  .test .bg:before {    content: "";    position: absolute;    background: orange;    z-index: -1;    top: 0;    left: 0;    bottom: 0;    right: 0;    border-bottom-right-radius: 120px;    transform: skewy(-4deg);    transform-origin: left bottom; }
<html>    <head>        <link rel="stylesheet" href="css/style.css">    </head>    <body>        <div class="test">            <div class="bg"></div>        </div>    </body></html>

How to make a rounded triangle using clip path

Instead of using a polygon as a clipping path I am using a path: a triangle with rounded corners:

.triangle {  padding: 0;  background-image: url(https://assets.codepen.io/222579/beagle400.jpg);  background-size: cover;  width:100px;  height: 100px;  -webkit-clip-path: url(#clip);  clip-path: url(#clip);}
.shadow { filter: drop-shadow(1px 6px 3px rgba(50, 50, 0, .4));}
<svg height="0" width="0" class="svg-clip" style="position:absolute">    <defs>         <clipPath id="clip">           <path d="M100.000,21.000 Q100,0 81.217,9.391L18.783,40.609 Q0,50 18.783,59.391L81.217,90.609 Q100,100 100.000,79.000Z" />        </clipPath>    </defs></svg> <div class="shadow">  <div class="triangle"/></div>

clip-path polygon with curve edges

Maybe another way to do that?