Edit in JSFiddle

<div class="container">
		<h2>Oh! You want to unsubscribe?</h2>
		<p>We hate goodbyes, But if you change yor mind, we'll always be here with something fun to share.</p>
		<a href="" class="btn" id="unsubscribe">Unsubscribe</a>
		<a href="" class="btn btn-light" id="cancel">Cancel</a>

		   	<br>
		   	<br>

	   <div class="emoji shocked">
	      <figure class="face">
	        <span class="eyes">
	          <span class="eye"></span>
	          <span class="eye"></span>
	        </span>
	        <span class="mouth">
	        </span>
	      </figure>
	    </div>

	</div>
	
	
	<footer style="position: absolute; bottom:10px; left: 10px;">By <a href="https://newtodesign.com" target="_top">NewToDesign</a></footer>
/*------ Base styles ------*/
body {
  background: #f7f8f9;
  font-family: arial;
  background-color: #FFF9DE;
  text-rendering : optimizeLegibility;
  -webkit-font-smoothing : antialiased;
}


.container {
  max-width: 500px;
  height: auto;
  margin: 50px auto;
  padding: 60px;
  padding-bottom: 20px;
  background-color: #fff;
  box-sizing: border-box;
  text-align: center;
  border-radius: 10px;
  box-shadow: 0px 15px 15px -12px rgba(0,0,0,0.09);
}

.btn {
  background-color: #F2DD68;
  text-decoration: none;
  padding: 15px 20px;
  font-weight: bold;
  border-radius: 50px;
  color: #fff;
}

.btn-light {
  background-color: #eee;
  color: #222;
}

.btn:hover{
  opacity: 0.8;
}

h2 {
  margin: 0;
  padding: 0;
  color: #444;
}

p {
  margin-top: 10px;
  line-height: 24px;
  margin-bottom: 40px;
  color: #888;
}

/*------ Main Emoji Styling ------*/

.emoji {
  box-sizing: border-box;
  margin: 30px auto 20px;
  width: 120px;
  height: 120px;
}

.face {
  width: 100px;
  height: 100px;
  position: relative;
  margin: 0 15px 30px 0;
  border-radius: 50%;
  background: #F2DD68;
  transition: 1s;
}

.face:after {
  content: '';
  display: block;
  position: absolute;
  width: 100%;
  height: 100%;
  top: -8px;
  left: -8px;
  border-radius: 50%;
  box-shadow: 8px 8px 0 0 rgba(0, 0, 0, 0.07);
}

.eye {
  position: absolute;
  width: 14px;
  height: 14px;
  top: 30px;
  left: 18px;
  z-index: 1;
  border-radius: 50%;
  background: #995710;
}

.eye:last-child {
  left: auto;
  right: 18px;
}

.emoji .eyed {
  animation-name: blink;
  animation-iteration-count: infinite;
  animation-duration: 3s;
}

@keyframes blink {
  10% {
    height: 10px;
    top: 32px;
  }
  20% {
    height: 0.5px;
    top: 37px;
  }
  50% {
    height: 10px;
    top: 32px;
  }
}

.mouth {
  position: absolute;
  top: 50px;
  left: 0;
  right: 0;
  z-index: 1;
  width: 70px;
  height: 34px;
  margin: 0 auto;
  border-radius: 0 0 70px 70px;
  overflow: hidden;
  background: #995710;
  transition: 0.3s;
}

.mouth:before,
.mouth:after {
  content: '';
  position: absolute;
  display: block;
}


/*------ Shocked Emoji Styling ------*/

.shocked .mouth {
  width: 25px;
  height: 25px;
  border-radius: 50%;
}


#cancel:hover ~ .emoji .mouth{
  top: 55px;
  z-index: 1;
  width: 50px;
  height: 25px;
  margin: 0 auto;
  border-radius: 0 0 70px 70px;
  overflow: hidden;
  background: #995710;
}

#unsubscribe:hover ~ .emoji .mouth{
  width: 50px;
  height: 5px;
  top: 60px;
  border-radius: 50px;
}