One way to do this, it is to create the API with your preferred back-end tools and deploy it to your local environment or to your favorite / available cloud provider.
That could be a lot of work when you only want some quick server and are more interested in your front-end code.
For those cases reqres.in comes in to the rescue!
The writing operations are not really creating or updating data, but they will return different responses.
It's open source and you can access the code in github
You can use your favorite API test tool (like Postman) and give it a try.
Do you have any other tools for API mockups? Let me know in the comments!