Deleting it probably isn’t the right move, since your website depends on jQuery. After all, if your site didn’t depend on jQuery, then the mixed content issue wouldn’t be giving you grief to begin with.
You need to ensure you do not have any resources on your website that are loaded over insecure URLs (http://).
Any that you find need to be replaced with secure variants (https://).
The reason that your site is blank over HTTPS is because your body has a display: none; style set, presumably because of your WordPress theme or plugins that make it appear using jQuery. This issue is 100% related to your usage of WordPress, so you’ll need to work through each instance of mixed content and repair it in your theme.