I'm not aware of a tutorial or example that will give you exactly what you want, but I'm not really surprised at that. Anyone who wants to create a simple REST service would choose to use a framework, and you don't want to do that. By choosing to build something yourself from the ground up, you're choosing complexity - exactly the complexity that the frameworks exist to remove.
The same is true for Java - virtually nobody creates raw REST services on top of HttpServlet, because using a framework makes much more sense.
Having said that, creating a "raw" REST service in Scala would be virtually identical to doing so in Java. So find a Java/Maven example and do the small amount of work necessary to turn it into something that runs on top of Scala and SBT. This would be a good starting point.