Hi, I always had this problem with cart: when user clicks the "x" button to remove a product, absolutely nothing happens.
There might be some js error on your website.
Please check the js erro refer:
https://codex.wordpress.org/Using_Your_Browser_to_Diagnose_JavaScript_Errors
Also share the screenshot of the errors and also share the site url and the admin credentials to check.
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Yes I could see the issue on your website but unfortunately I was unable to find the reason for the issue.
Based on previous user issues it seems to be a caching related issue, so please try deactivating the caching plugin and also try clearing the server cache.
Let me know if this helps.