Edit in JSFiddle

var pomCircle = function() {

  $('.pomProgressTimer').circleProgress({
    value: 1.0,
    thickness: '25',
    size: 50,
    fill: {
      color: '#FF6347',
    },
    animation: {
      duration: 30000,
    },
  })
  

};

$('#start-countdown').on('click', function() {
  pomCircle();

});

$('#pause-countdown').on('click', function() {
 var el = $('.pomProgressTimer');
    $(el.circleProgress('widget')).stop();

});

$('#resume-countdown').on('click', function() {
  var obj = $('.pomProgressTimer').data('circle-progress'),
    progress = obj.lastFrameValue;
    $('.pomProgressTimer').circleProgress({
    animationStartValue: progress,
  });

});

<div class="container">
  <div class="pomProgressTimer">
  </div>
  <button id="start-countdown">
    Play</button>
  <button id="pause-countdown">
    Pause</button>
  <button id="resume-countdown">
    Resume</button>
</div>