You should use destroy:
$('#slideshow').cycle('destroy');
BTW, you should debounce a little the resize method using a timeout:
jQuery(document).ready(function () {
jQuery('#slideshow').cycle({
fx: 'scrollHorz',
timeOut: '4000'
});
var resizeTimeout;
window.onresize = function (event) {
clearTimeout(resizeTimeout);
resizeTimeout = setTimeout(function () {
jQuery('#slideshow').cycle('destroy');
jQuery('#slideshow').cycle({
fx: 'scrollHorz',
timeOut: '4000'
});
}, 50);
};
});