Angular - trouble with splicing an array

I'm pretty new to AngularJS so I'm sure I'm just making a simple mistake.

I want to splice the cardTypes array on the var newCard = cardTypes.shift(); line rather than using .shift() so I can take account of my ng-repeat index.

It works fine with .shift() but no data comes through at all if I try .splice(index, 1).

Any help would be greatly appreciated.

    .controller('CardsCtrl', function($scope, $ionicSwipeCardDelegate) {
  var cardTypes = [
    { title: 'Swipe down to clear the card', image: 'img/pic.png' },
    { title: 'Where is this?', image: 'img/pic.png' },
    { title: 'What kind of grass is this?', image: 'img/pic2.png' },
    { title: 'What beach is this?', image: 'img/pic3.png' },
    { title: 'What kind of clouds are these?', image: 'img/pic4.png' }
  ];

  $scope.cards = Array.prototype.slice.call(cardTypes, 0, 0);

  $scope.cardSwiped = function(index) {
    $scope.addCard();
  };

  $scope.cardDestroyed = function(index) {
    $scope.cards.splice(index, 1);
      $scope.addCard();
  };

  $scope.addCard = function() {
    var newCard = cardTypes.shift();
    newCard.id = Math.random();
    $scope.cards.push(angular.extend({}, newCard));
  }
})

.controller('CardCtrl', function($scope, $ionicSwipeCardDelegate) {
  $scope.goAway = function() {
    var card = $ionicSwipeCardDelegate.getSwipebleCard($scope);
    card.swipe();
  };
});