This article refers to Event Websites built in the Modern Event Website Builder (not the Legacy Event Website Builder).
Currently, you can't clone event websites created in the Modern Event Website Builder, but you can save Layouts and re-use them (which achieves much the same outcome).
To save Layouts, go into the Builder of the event website you want to clone from.
Open each page, and in the bottom-right toolbar, click the "up" arrow next to the word Update to see other options, then select "Save Layout".
In your new event, in the Modern Event Website Builder, create blank pages and create your menu as you want it to appear.
Then go into each page, and click on "Add a New Block".
When the new block pop-up opens, click on the "Saved" (heart icon) tab.
In the left-hand panel, under "Library", select "Layouts" to see all your saved layouts. (You may need to wait for your Library to synch.)
Select the layout to import, and be sure to click on "Replace Global Styling" at the bottom, so the style will also be copied into your new page.
Then click "Import This Layout".
This will import the layout and styling of the page.
Remember to update the page.
Repeat for the other pages in your website.