It seems like the autoscroll constructor isn't chaining correctly, so isn't returning the instance of the scrollable you are creating.
Try changing your code slightly to get a reference to the API after it's been initialized:
var scrollableApi;
$(document).ready(function () {
// Initialize the slideshow
$('#slideshow')
.scrollable({ items: '.scrollable > .items', circular: true, mousewheel: false, speed: 1000 })
.navigator({ navi: "#slideshow > .scrollable-nav", naviItem: "a", activeClass: "current" })
.autoscroll({ interval: 1000, autopause: true, api: true });
// get a reference to the API
scrollableApi = $('#slideshow').data('scrollable');
// Pause the slideshow when the link is clicked
$("#pauseSlideshow").click(function () {
scrollableApi.pause();
});
});