In this article, I am sharing code snippets to create List items and update items with Taxonomy or Managed Metadata field on a custom list. I have seen some threads on how to update the multi-value taxonomy fields also. The below code demonstrates both single/multi-valued, taxonomy column update snippets via JSOM.
Create List Item 

Let us quickly test this via Chrome Developer Console.

Go to page and view site in the Classic experience.
Press F12. Go to Developer Console and paste the above code in the console.
Press Enter.
We should get an undefined logged-in console. Don’t worry. Ignore this message.
Now let us try this out, call this function in chrome console developer like below
If you get the above message, an item will be created in the list and the Taxonomy field would have been set. Please refer to the below screenshot for reference.
The same way, you can try multi-value also by passing the parameter as false in the CreateItem method.
Update Item

Use the same Chrome Developer Console technique to quickly test this function. Type ”UpdateItem(8,false)”. Please note that we are updating the same item created using CreateItem method.

Calling update method
Update Taxonomy Or Managed Metadata Field Via SharePoint JSOM
Update Taxonomy Or Managed Metadata Field Via SharePoint JSOM